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Bubble Rap: Forwarding in Small World DTNs Finbar Lynch Care of David Lodge University of Rummidge [email protected] Maurice Zapp Cyber Science Lab Euphoric State University [email protected] P ABSTRACT In this paper we seek to improve understanding of the structure of human mobility, and to use this in the design of forwarding algo- rithms for Delay Tolerant Networks for the dissemination of data amongst mobile users. Cooperation binds but also divides human society into commu- nities. Members of the same community interact with each other preferentially. There is structure in human society. Within society and its communities, individuals have varying popularity. Some people are more popular and interact with more people than oth- ers; we may call them hubs. Popularity ranking is one facet of the population. In many physical networks, some nodes are more highly connected to each other than to the rest of the network. The set of such nodes are usually called clusters, communities, cohe- sive groups or modules. There is structure to social networking. Different metrics can be used such as information flow, Freeman betweenness, closeness and inference power, but for all of them, each node in the network can be assigned a global centrality value. What can be inferred about individual popularity, and the struc- ture of human society from measurements within a network? How can the local and global characteristics of the network be used prac- tically for information dissemination? We present and evaluate a sequence of designs for forwarding algorithms for Pocket Switched Networks, culminating in Bubble, which exploit increasing levels of information about mobility and interaction. 1. INTRODUCTION The first generation of human network models were probably the Erdos-Renyi random graphs [3]. More recently, heterogene- ity has been introduced into models through the use of power-law and small-world graphs, especially in analysis of the AS-level of the Internet, for example in [5] [6]. This is the second genera- tion of modeling. It is well known that some nodes may be more highly connected to each other than to the rest of the network. The set of such nodes are usually called clusters, communities, cohe- sive groups or modules. Many different approaches to commu- nity detection in complex networks have been proposed such as k- clique [19], betweenness [17], modularity [16] and more recently Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Copyright 200X ACM X-XXXXX-XX-X/XX/XX ...$5.00. information theory [21]. Other kind of methods can be found in the survey paper [15]. Community detection can help us understand the local structure in mobility traces, and therefore help us design good strategies for information dissemination. It may be that com- munities detected from mobility data do not actually match well to real social communities, but still help with improved forwarding. 1 . The first goal of this research is to move to a third generation of human mobility models, understanding heterogeneity at multiple levels of detail. Wireless networking has moved from a first generation of wire- less access provided by 802.11 LANs and cellular services, through a second generation of Mobile Ad Hoc Networking, now on to a third generation: Pocket Switched Networks(PSN) [10] are a cat- egory of Delay Tolerant Network [8] aimed at supporting applica- tions for human-to-human communications, through the so-called ferrying paradigm. Previous work [4] established the inter-contact intervals, and contact durations for a wide range of typical human mobility patterns and for a variety of today’s radio devices. Crit- ically, it was shown that stateless forwarding schemes would not provide a bounded expected mean delivery latency across such sys- tems. On the other hand, flooding packets has a very high cost, not just in link-utilisation, but for other resources such as node storage and battery life, which are likely to be highly valued by users. The second goal of this research is to devise efficient forward- ing algorithms for PSNs which take advantage of both a priori and learned knowledge of the structure of human mobility, to provide improved performance trade-off between delivery probability, la- tency and cost. Society naturally divides into communities according to needs for cooperation or selection. In sociology, the idea of “correlated interaction” is that an organism of a given type is be more likely to interact with another organism of a same type than with a randomly chosen member of the population [18]. If the correlated interaction concept applies, then our intuition is that using this community in- formation to influence forwarding paths may be advantageous. To date, though, there have been few results to support this conjecture that we are aware of, except a very preliminary analysis by Hui et al. [11] on the use of as users’ affiliation. Searching using node degree rank was first introduced for peer- to-peer networks. Adamic et al. [1] describe a method for searching in networks, where the node degrees follow a power-law distribu- tion, when the power law coefficient is sufficiently close to 2. Their strategy is to choose a node at each step with highest degree among all neighbors of the current node, quickly finding the highest de- gree node. Once the highest degree node has been visited, it will be avoided, and a node of approximately second highest degree will be 1 We will find out later that they actually match quite well. 1

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Page 1: Bubble Rap: Forwarding in Small World DTNsjac22/haggle/.communism.pdf · Bubble Rap: Forwarding in Small World DTNs Finbar Lynch Care of David Lodge University of Rummidge Finbar.Lynch@small.world.edu

Bubble Rap: Forwarding in Small World DTNs

Finbar LynchCare of David Lodge

University of [email protected]

Maurice ZappCyber Science Lab

Euphoric State [email protected]

Paper 102

ABSTRACTIn this paper we seek to improve understanding of the structure ofhuman mobility, and to use this in the design of forwarding algo-rithms for Delay Tolerant Networks for the dissemination of dataamongst mobile users.

Cooperation binds but also divides human society into commu-nities. Members of the same community interact with each otherpreferentially. There is structure in human society. Within societyand its communities, individuals have varying popularity. Somepeople are more popular and interact with more people than oth-ers; we may call them hubs. Popularity ranking is one facet ofthe population. In many physical networks, some nodes are morehighly connected to each other than to the rest of the network. Theset of such nodes are usually called clusters, communities, cohe-sive groups or modules. There is structure to social networking.Different metrics can be used such as information flow, Freemanbetweenness, closeness and inference power, but for all of them,each node in the network can be assigned a global centrality value.

What can be inferred about individual popularity, and the struc-ture of human society from measurements within a network? Howcan the local and global characteristics of the network be used prac-tically for information dissemination? We present and evaluate asequence of designs for forwarding algorithms for Pocket SwitchedNetworks, culminating in Bubble, which exploit increasing levelsof information about mobility and interaction.

1. INTRODUCTIONThe first generation of human network models were probably

the Erdos-Renyi random graphs [3]. More recently, heterogene-ity has been introduced into models through the use of power-lawand small-world graphs, especially in analysis of the AS-level ofthe Internet, for example in [5] [6]. This is the second genera-tion of modeling. It is well known that some nodes may be morehighly connected to each other than to the rest of the network. Theset of such nodes are usually called clusters, communities, cohe-sive groups or modules. Many different approaches to commu-nity detection in complex networks have been proposed such as k-clique [19], betweenness [17], modularity [16] and more recently

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.Copyright 200X ACM X-XXXXX-XX-X/XX/XX ...$5.00.

information theory [21]. Other kind of methods can be found in thesurvey paper [15]. Community detection can help us understandthe local structure in mobility traces, and therefore help us designgood strategies for information dissemination. It may be that com-munities detected from mobility data do not actually match well toreal social communities, but still help with improved forwarding.1.

The first goal of this research is to move to a third generationof human mobility models, understanding heterogeneity at multiplelevels of detail.

Wireless networking has moved from a first generation of wire-less access provided by 802.11 LANs and cellular services, througha second generation of Mobile Ad Hoc Networking, now on to athird generation: Pocket Switched Networks(PSN) [10] are a cat-egory of Delay Tolerant Network [8] aimed at supporting applica-tions for human-to-human communications, through the so-calledferrying paradigm. Previous work [4] established the inter-contactintervals, and contact durations for a wide range of typical humanmobility patterns and for a variety of today’s radio devices. Crit-ically, it was shown that stateless forwarding schemes would notprovide a bounded expected mean delivery latency across such sys-tems. On the other hand, flooding packets has a very high cost, notjust in link-utilisation, but for other resources such as node storageand battery life, which are likely to be highly valued by users.

The second goal of this research is to devise efficient forward-ing algorithms for PSNs which take advantage of both a priori andlearned knowledge of the structure of human mobility, to provideimproved performance trade-off between delivery probability, la-tency and cost.

Society naturally divides into communities according to needsfor cooperation or selection. In sociology, the idea of “correlatedinteraction” is that an organism of a given type is be more likely tointeract with another organism of a same type than with a randomlychosen member of the population [18]. If the correlated interactionconcept applies, then our intuition is that using this community in-formation to influence forwarding paths may be advantageous. Todate, though, there have been few results to support this conjecturethat we are aware of, except a very preliminary analysis by Hui etal. [11] on the use of as users’ affiliation.

Searching using node degree rank was first introduced for peer-to-peer networks. Adamic et al. [1] describe a method for searchingin networks, where the node degrees follow a power-law distribu-tion, when the power law coefficient is sufficiently close to 2. Theirstrategy is to choose a node at each step with highest degree amongall neighbors of the current node, quickly finding the highest de-gree node. Once the highest degree node has been visited, it will beavoided, and a node of approximately second highest degree will be

1We will find out later that they actually match quite well.

1

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chosen. Effectively, after a short initial climb, the search descendsthe degree sequence. The claim is that this is the most efficient wayto do this kind of sequential search. This is a good incentive for usto look at this approach in PSNs as well. However, as we know,a PSN is very different from the Internet, which is largely fixed instructure. A PSN is a dynamic temporally varying network [12];nodes move, connect and depart from time to time; the concept ofdegree is not simple to define. Is the degree of a node in a PSN thenumber of other nodes it has met in one second, one minute, onehour or one day? Why not 6 hours?

Freeman [9] defined several centrality metrics to measure the im-portance of a node to the network. “Betweenness” centrality mea-sures the number of times a node falls on the shortest path betweentwo other nodes. This concept is also valid in a temporal network.In a PSN, it can represent the importance of a node for relayingtraffic for others in the system. Hence, we will look at whether thehierarchical search works with this centrality metric, and how toacquire the metric in a practical, decentralised way.

There are six specific contributions in this paper that progresstowards our two top-level goals. First, we use the correlation ofcontact duration and number of contacts to classify human rela-tionships in a PSN into four categories. Second, we use k-cliquecommunity detection algorithms on several real traces, to explorethe nature of human community in different mobile environments.Third, we show empirically that identifying nodes according totheir centrality or ranking can improve delivery cost-effectivenessover a greedy approach. Fourth, we reconfirm the result of Hui etal. [11] that labelling increases the delivery cost-effectiveness, byusing more reliable node selection. Fifth, we combine communityand ranking together, making use of both local and global struc-tures. This reduces the dead-end effect caused by global ranking,by forming a hybrid forwarding strategy, which improves over thedelivery performance of naive multiple-copy-multiple-hop floodingschemes, but with much lower cost. Sixth, we use average unit-timedegree to approximate centrality, and show that this achieves nearlythe same performance as greedy ranking.

2. METHODOLOGY2.1 Experimental Data Sets

We use four experimental data sets gathered by the Haggle Projectby two years referred to as Hong-Kong, Rummidge, Infocom05,Infocom06, and one other dataset from the MIT Reality MiningProject [7], referred to as Reality. Previously the characteristics ofthese datasets such as inter-contact and contact distribution, havebeen explored in several studies [4] [10] [14], to which we refer thereader for further background information.

• In Hong-Kong, the people carrying the wireless devices werechosen independently in a Hong-Kong bar, to avoid any par-ticular social relationship between them. These people havebeen invited to come back to the same bar after a week. Theyare unlikely to see each other during the experiment.

• In Rummidge, the iMotes were distributed mainly to two groupsof students from University of Rummidge Computer Labo-ratory, specifically undergraduate year1 and year2 students,and also some PhD and Masters students. In addition to this,a number of stationary nodes were deployed in various lo-cations that is expected many people to visit, such as gro-cery stores, pubs, market places, and shopping centers inand around the city of Rummidge, UK. However, the dataof these stationary iMotes will not be used in this paper. Thisdataset covers 11 days.

• In Infocom05, the devices were distributed to approximatelyfifty students attending the Infocom student workshop. Par-ticipants belong to different social communities (dependingon their country of origin, research topic, etc.). However,they all attended the same event for 4 consecutive days andmost of them stayed in the same hotel and attended the samesections (note, though, that Infocom is a multi-track confer-ence).

• In Infocom06, the scenario was very similar to Infocom05 ex-cept that the scale is larger, with 80 participants. Participantswere selected so that 34 out of 80 form 4 subgroups by aca-demic affiliations. In addition, 20 more long range iMoteswere deployed at several places in the conference site to actas access points. However, the data from these fixed nodes isalso not used in this paper.

• In Reality, 100 smart phones were deployed to students andstaff at MIT over a period of 9 months. These phones wererunning software that logged contacts with other Bluetoothenabled devices by doing Bluetooth device discovery everyfive minutes, as well as logging information about the cellu-lar tower they are associated with (a total of 31545 differenttowers were logged).

The five experiments are summarised in Table 1.

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Figure 1: Number of contacts versus the contact durations forpairs of Rummidge Students.

2.2 HaggleSim EmulatorIn order to evaluate different forwarding algorithms, we used

an emulator called HaggleSim [11], which can replay the mobil-ity traces collected and emulate different forwarding strategies onevery contact event. This emulator is completely driven by contactevents. The original trace files are divided into discrete sequentialcontact events, and they are fed into the emulator as inputs. Theevent granularity depends on our choice of balance between replayspeed, and the degree of accuracy desired. Here we use a granu-larity of 100 seconds. The emulator reads the source file line byline, treating each line as a discrete encounter event, and makes aforwarding decision on this encounter based on the forwarding al-gorithm under study. A snapshot of the source file and details about

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Experimental data set Infocom05 Hong-Kong Rummidge Infocom06 RealityMiningDevice iMote iMote iMote iMote Phone

Network type Bluetooth Bluetooth Bluetooth Bluetooth BluetoothDuration (days) 3 5 11 3 246

Granularity (seconds) 120 120 600 120 300Number of Experimental Devices 41 37 54 98 97

Number of External Devices 264 868 11,357 14,036 0Number of internal contacts 22,459 560 10,873 191,336 54,667Average # Contacts/pair/day 4.6 0.084 0.345 6.7 0.024Number of external contacts 1,173 2,507 30,714 63,244 0

Table 1: Characteristics of the five experimental data sets

removing artificial temporal ordering created by the file format canbe found in [11].

For each emulation in this paper, 1000 messages are created, uni-formly sourced between all node pairs. And each emulation is re-peated 20 times with different random seeds for statistical confi-dence. We analysed the delivery success rate, the delivery cost, thedelay distribution, the hop distribution of all successful deliveries,and the popularity of a node as a relay, based on the log files pro-duced by the emulator.

3. CHARACTERISTICS OF OUR CONTACTGRAPHS

Our first contribution is to introduce the notion of “contact graph”as a way to help represent the mobility traces, and to choose athreshold for community detection. The way we convert humanmobility traces into weighted contact graphs is based on the num-ber of contacts and the contact duration, although we could useother metrics. The nodes of the graphs are the physical nodes fromthe traces, and the edges are the contacts. The weight of the edgesare the values based on the metrics specified such as the number ofcontacts during the experiment.

We measure the relationship between two people by how manytimes they meet each other and also how long they stay with each.We naturally think that if two people spend more time together orsee each other more often, they are in closer relationship. In thiswork we are not going to provide a specific threshold to infer actualsocial context: we just use these two metrics to produce some mapswhich are useful to guide forwarding.

Here we explore further properties of the experimental scenar-ios, and present statistics concerning the contact graphs for eachdataset.

3.1 Weight Distribution of Contact GraphsFirst we would show that the statistical properties for the two

conference scenario are quite similar. Figure 2(a) and 2(b) showthe contact duration distribution for Infocom06 and Infocom05 re-spectively. We can see that their distributions are quite similar, witha mean different as small as 0.0003(0, 0.0633). More similaritieswill be seen in the next section as well. Because of space limita-tion, and these similarities, the later sections we only selectivelyshow one as example, in most cases Infocom06, since it containsmore participants, We show more results in a separate technical re-port.

3.2 Correlation between Regularity and Fa-miliarity

We assume contact duration indicates familiarity. Two peoplesharing the same office might hate each other, and not talk, but

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Figure 2: Contact duration distribution for Infocom06 and In-focom05

we will ignore this kind of extreme situation here. The number oftimes two people meet each other implicitly reveals the pattern withwhich they meet. In this work, we infer regularity of meetings fromthe number of contacts. Two people might meet a lot of times in ashort period (e.g. a day), and then not at all. However, short periodswith many contacts are less likely to contribute to the upper quartersof the distribution, and here we will ignore these too as outliers.

Figure 1 shows the correlation between regularity and familiarityin the Rummidge data set. Here the regularity is positively corre-lated to the familiarity with a correlation coefficient of 0.9026. Wedefine four kinds of relationships between a pair of nodes: Com-munity, Familiar Strangers, Strangers, and Friends. A pair of nodeswhich has long contact duration (high familiarity) and large num-ber of contacts (high regularity) is likely to belong to the same com-munity. A pair of nodes which meet regularly but don’t spend timewith each other, could be familiar strangers [20] meeting everyday.People who don’t meet regularly and don’t spend time with eachother would be in the category of strangers. Finally, for node pairswhich don’t meet very frequently but spend quite a lot of time to-gether for each meeting, we count as friends. It is not necessarythat the division of the four quarters are exactly at the middle. Itis here acting as a reference or example. A clear cut division mayneed more empirical experimental results. But here we provide themethodology to classify these four kind of relationship based onpure contact duration and frequency. Additional difficulties facedby empirical social network research are well described in work byWatts [24].

Figure 3 shows the correlation between the number of contactsand contact durations for the other four experiments. We can seethat conference environments are quite similar, both with a narrowstripe in the left bottom quarter. This stripe shows that people inthe conference tend to meet each other more often than spend long

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Figure 3: Number of contacts against contact durations for allpairs in the four datasets, with correlation coefficient.

time together. That is typical conference scenario, since peoplemay meet each other many times in coffee breaks, corridors, regis-tration desk etc. They may stand together and chat for a while, andthen shift to chat with others instead of spending all the times to-gether. Infocom06 contains double the number of participants, andhence more data points. The Reality set is similar to the Rummidgeone, with most of the points lying on or above the diagonal line.However, it also seems that people have more contacts instead ofspending times together. In the HongKong figure, we can find twopairs of friends, two pairs of close community members, and twopairs of familiar strangers. All the other pairs lie in the strangersquarter. This is in line with our expectations for an experiment de-signed to contain little social correlation.

4. ON HUMAN HETEROGENEITYIn many mobility models such as the random way-point, nodes

are assumed, explicitly or implicitly, to have homogeneous speeddistributions, importance and popularity. Our intuition is that thelast two assumptions, at least, are not true. People have differ-ent levels of popularity: salesmen and politicians meet customersfrequently, whereas computer scientists may only meet a few oftheir colleagues once a year. Homogeneity might favour differentforwarding strategies for PSNs. In contrast, we want to employheterogeneous popularity to help design more efficient forwardingstrategies: we prefer to choose popular hubs as relays rather thanunpopular ones. To date we are not aware of any empirical evidencefor using human popularity or node centrality for information dis-semination in mobile networks.

A temporal network is a kind of weighted network. The cen-trality measure in the traditional weighted network may not workhere since the edges are not necessary concurrent. Hence we needa different way to calculate the centrality of each node in the sys-tem. Our approach is as follows: First we carried out a large num-ber of emulations of unlimited flooding with different uniformlydistributed traffic patterns created using the HaggleSim emulator.Then we count the number of times a node acts as a relay for othernodes on all the shortest delay deliveries. Here the shortest de-lay delivery refers to the case when a same message is deliveredto the destination through different paths, where we only count thedelivery with the shortest delay. We call this number the “between-

ness centrality” of this node in this temporal graph2. Of course,we can normalize it to the highest value found. Here we use un-limited flooding since it can explore the largest range of deliveryalternatives with the shortest delay. We believe that this definitionis similar in spirit to the definition of the Freeman centrality [9].

Initially, we only consider a homogeneous communications pat-tern, in the sense that every destination is equality likely, and wedo not weight the traffic matrix by locality. We then calculate theglobal centrality value for the whole homogeneous system. Later,we will analyze the heterogeneous system, once we have under-stood the community structure.

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Figure 4: Number of times a node as relays for others on fourdatasets.

Figure 4 shows the number of times a node fall on the shortestpaths between all other node pairs. We can simply treat this as thecentrality of a node in the system. We observed a very wide het-erogeneity in each experiment. This clearly shows that there is asmall number of nodes which have extremely high relaying abil-ity , and a large number of nodes have moderate or low centralityvalues, across all experiments. One interesting point from the HKdata is that the node showing highest delivery power in the figureis actually an external node. This node could be some very popularhub for the whole city, i.e. postman or a newspaper man in a pop-ular underground station, which relayed a certain amount of crosscity traffic. The 30, 70 percentiles and the means of normalizedindividual node centrality are shown in Table 2.

Experimental data set 30 percentile Mean 70 percentileRummidge 0.052 0.220 0.194

Reality 0.005 0.07 0.05Infocom06 0.121 0.188 0.221Hong Kong 0 0.017 0

Table 2: Statics about normalized node centrality in 4 experi-ments

2We have calculated the weighted node centrality for each node,but found out that the weighted centrality is not well correlatedto the centrality on the temporal graph. Nodes have very highweighted centrality may have very low temporal centrality.

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5. FINDING K-CLIQUE COMMUNITIESOur second contribution is the identification of community struc-

tures using k-cliques. We have calculated all the results by usingboth contact duration and number of contacts on all five experi-ments but because of space limitations we just show two cases ofcontact duration and two cases of number of contacts.

5.1 K-Clique Community DetectionWe use the k-clique community algorithm proposed by Palla et

al. [19] in their work, since overlapping of communities are al-lowed, and we believe that in human society one person may be-long to multiple communities. They define a k-clique communityas a union of all k-cliques (complete subgraphs of size k) that canbe reached from each other through a series of adjacent k-cliques,where two k-cliques are said to be adjacent if they share k-1 nodes.Their definition is based on their observation that an essential fea-ture of a community is that its members can be reached throughwell-connected subsets of nodes, and that there could be other partsof the whole network that are not reachable from a particular k-clique, but they potentially contain further k-clique communities.

To illustrate this further, the k-clique-communities of a networkat k = 2 are equivalent to the connected components, since a 2-clique is simply an edge and a 2-clique-community is the union ofthose edges that can be reached from each other through a seriesof shared nodes. Similarly, a 3-clique-community is given by theunion of triangles that can be reached from one another through aseries of shared edges. As k is increased, the k-clique-communitiesshrink, but on the other hand become more cohesive since theirmember nodes have to be part of at least one k-clique. The methodis used for a binary network, and a weighted network is turned intobinary network by setting a threshold.

5.2 K-Clique University CommunitiesIn the visualization, an edge is added between two nodes if they

are direct neighbors to each other in the community. The length ofthe edges is not proportional to any property of either the commu-nities or the nodes. However the width of the edges is proportionalto the link-weight that is the number of shared nodes between thetwo communities.

Figure 5 shows the k-clique communities detected from the Rum-midge student data using number of contacts.

K = 3 K = 4

K = 5 K = 10

Figure 5: Communities based on number of contacts withweight threshold =29, k=3,4,5, and 10 (Rummidge).

The duration of the experiment is 11 days. For the number ofcontacts, we used a threshold of 29 contacts, which represents an

average of 3 contacts per day.3 In this case, around 8.5% of all theedges are taken into account. We observe that the nodes mainlysplit into two communities of size 11 respectively with k as high as10. Next we examine lower values of k. We can see also from Fig-ure 5, when k = 3 there is a big community of 31 nodes, and whenk = 4 the big community splits into two overlapping communi-ties of sizes 14 and 17 with overlapping size = 1, and when k = 5

the two overlapping communities split into two disjoint communi-ties of size 14 and 16 respectively. The two disjoint communitystructures stay visible until k = 11, with a gradual decrease in thecommunity size. For the contact duration metric, we set the contactduration threshold to be 10 hours for the whole 11 days of exper-iment. We also observe mainly two communities when using thismetric. The membership of these two communities is more or lessthe same as that when using the number of contacts metric. Thisagrees with Figure 1 that the contact duration and number of con-tacts for Rummidge data is highly correlated.

The output from the algorithm clearly illustrates that the partici-pants can be seen as two communities in this case. When we look atthe experimental data, the two communities classified by this algo-rithm match well with the two groups of Year1 and Year2 studentsselected for the experiment. Of course, in each group of studentstend to know each other and meet each other, and hence the cliquesize can be as large as 10.

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Figure 6: Communities based on contact durations with weightthreshold = 648000 seconds, k=3,4 (Reality).

5.3 K-clique Communities in Reality MiningThis is another campus environment but the environment is more

diverse than the Rummidge one. Out of 100 participants, 75 are ei-ther students or faculty in the MIT Media Laboratory, while the re-maining 25 are incoming students at the adjacent MIT Sloan busi-ness school. Of the 75 users at the Media lab, 20 are incomingmasters students and 5 are incoming MIT freshmen. So we cansee unlike the Rummidge data consisting mainly of two classes ofstudents, this dataset consists of more groups.

First we look at communities detected by using threshold of388800 seconds or 108 hours on the 9 months Reality Mining dataset.Here we assume 3 lectures per week and 4 weeks per month and3Considering some students may be taking the same courses, bein the same supervision group, and live in the same College, andhence using same dining hall, this value is reasonable.

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for a total of 9 months, we get this threshold value (2% of the totallinks are taken into consideration). Research students in the sameoffice may stay together all the time a day so their contact durationthreshold could be very large. For students attending lectures, thisestimation can be reasonable. A looser threshold still detects thelinks with much stronger fit. We observe 8 communities of size(6,3,7,7,16,5,4,7) when k = 3 in this case. The 4-size one overlapat one node with the 16-size which also overlap with another 7-size community at another nodes. Two other 7-size nodes overlapeach other with overlapping size 1. The other three communitiesare disjoint. When k = 4, the 3-clique community is eliminatedand other communities shrink or are eliminated, and only 5 com-munities of size (4,13,5,5,7) left. All of these 5 communities aredisjoint. When k = 5, 3 communities of size (9,6,5) remains, the9-size one and the 5-size one are split from the 13-size one in the 4-clique case. Moving to k = 6 and k = 7, there are 2 communitiesand 1 community respectively.

We are also interested in knowing about small groups which aretightly knit. We set a strict threshold of 648000 seconds, that is onaverage 1 hour per weekday, 4 weeks per month, and for a totalof 9 months. Around 1% of the links are taken into account forthe community detection. When k = 3, there are three disjointcommunities of size (12,7,3). When k = 4, there are only twocommunities left of size (8,6). Figure 6 shows the 3-cliques and4-clique communities of 648000 seconds threshold with its counterparts of 388800 seconds. A single 7-size community remains ink = 5 and k = 6 cases, this 7-clique community is the same asin the 388800 second case. These 7 people could be people from asame research group, they know each other and have long contactwith each.

5.4 K-clique Conference CommunitiesIn this section, we will show the community structures in a con-

ference environment. Here we take Infocom06 as an example sinceit contains more participants than Infocom05 and we have moreparticipants information. Infocom is a multiple-track conferencewith several programs running at the same time. We don’t expectall our 80 experimental participants to attend the same sessions, sowill not expect the clique size to be as big as the Rummidge data.The total dataset only covers 3 days, hence we will not expect thethreshold to be very big. People usually socialise during confer-ences in a small groups so we expect clique sizes of 3, 4 or 5 tobe reasonable. And for Infocom06, the participants were speciallyselected so that 34 out of 80 form four subgroups according to aca-demic affiliations. Out of these four groups, there were two groupsfrom institutes in Paris with size of four and ten respectively(namedParis Group A and Paris Group B), and there is one group fromLausanne Switzerland of five people, and another, larger group of15 people from the local organization in Barcelona. But for thislocal organization group, the volunteers are from different local in-stitutions and also responsible for different sessions in the confer-ence so we will not expect them to be all together. After collectingthe data, for privacy purpose, all the personal information about theparticipants are deleted except the Node ID, the affiliation and thenationality.

Figure 7 shows the 3-clique communities with threshold 20000seconds, that is approximately 1.85 hours per day. 1.68% of alledges are taken into account for the community calculation. Weobserve 6 communities of size (25,11,6,6,5,3) in this case. The 25-size one overlap at one node with a 6-size one which also overlapwith the 11-size community at another node and the 3-size one atanother node. The 2nd 6-size community also overlap the 3-sizeand 11-size at another two nodes. The 5-size community stands

alone. Although we know that during a conference where the peo-ple from different sub-communities tend to mix together and hencethe boundary of affiliation communities would become less clear.We still find the hints of the original affiliation communities fromthe figure. The algorithm correctly classified the nodes belongingto the local organizers into a community, see the Barcelona Groupat the right hand side of the figure, and also the members of theLausanne Group into another community. There are several nodeswhich not belonging to these affiliations are also “false positively”classified into the same communities, but this also truly reflects thenature of a conference, to socialize with people in other institutions.The two Paris groups are also clearly identified, they tend to social-ize with each other. Nodes 47 is belonging to both groups, from thesame figure, it is important to link this two groups together. Thereare many members in the 25-size group not belonging to a com-mon institution but they are here linked together by different smallgroups of mixing together in conference.

Barcelona GroupParis Group AParis Group BLausanne Group

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Figure 7: 3-clique communities based on contact durationswith weight threshold equals 20000 seconds (Infocom06).

When we increase k from 3 to 4, it splits into 8 communitiesof size (8,6,6,5,5,4,4,4). The number of nodes decrease a lot, butwe can also see that the tight of the affiliation communities arequite strong. The Barcelona Group and the Lausanne group arestill there, just the number change from 7 to 5 and 5 to 4 respec-tively. The links from node 47 linking two detected communitiescontaining Paris Groups members disappear, but we still observe amixing of five Paris Group A and Group B nodes together to forma community structure.

Barcelona Group (Spanish)Paris Group A (French)Paris Group B (French)

Italian

Figure 8: 5-clique communities based on contact durationswith weight threshold equals 20000 seconds (Infocom06).

Figure 8 shows the communities when k is equal to 5. Thereare now only 3 communities of size (5,5,5). All small communitiessize less than 5 in k = 4 case are eliminated. We can observe that theBarcelona Group and a Paris Group are still there. Another groupmainly consists of Italian speaking people overlaps with the French

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group. We do not want to claim that the division by the k-cliquecommunity algorithm matches perfectly to real social groups, butat least it gives us rich information about the underlying humaninteraction. A preliminary conclusion here is that, affiliation oreven nationality have a very strong tie to human contacts, even inthe conference, a highly mixed environment.

5.5 K-clique Metropolitan CommunitiesAs we can see from Figure 3, most pairs have low number of

contacts and contact duration. We didn’t expect to discover a richsocial structure from this data. However in this case, we can seehow some internal nodes without much social correlation are nev-ertheless connected together by external Bluetooth devices, by con-sidering all of the 869 nodes detected, including 37 iMotes and 832external devices.

The experiment lasted 6 days. First we set the threshold to be3 encounters which is equal to an average of one encounter per 2days, around 8% of the total links will are taken into consideration.In this case we observed 10 communities sized (8,4,3,18,3,10,6,5,6,3)respectively when k = 3, which is shown on the Figure 9.

Figure 9: Communities based on number of contacts withweight threshold = 3 and k=3 (HK).

From the same figure we also see that the internal nodes areusually joined together by external nodes. They themselves maynot have social correlation at all, but are connected together bythese unknown external devices which may belong to colleaguesor friends or familiar strangers of the iMote owners. This gives usoptimism about the possibility of city-wide PSN data communica-tion.

When k = 4 communities shrink to only two small communitiesof size 4 and 5 respectively. It seems that k = 4 is too strong inthis case. We tried to increase the number of contacts to be 6, onaverage one contact per day; in this case on 2.4% of the links aretaken into consideration. There are only 6 small communities ofsize (4,3,3,3,6,4) respectively, with only two overlapping with eachother at a single node. This again confirms the very sparse socialcohesion in the experiment.

6. INTERACTION AND FORWARDINGIn the first half of this paper we have shown the existence of het-

erogeneity at the level of individuals and groups, in all the mobilitytraces. This motivates us to consider a new heterogeneous model

of human interaction and mobility.

Categories of human contact patterns Human relationships canbe modelled by using correlation of contact duration andnumber of contacts. We defined four types of human re-lationship based on the correlation of contact duration andnumber of contact.

Cliques and Community We explored the community structuresinside different social environments, and found these com-munity structures match quite well to the real underlying so-cial structures.

Popularity Ranking We shall see that popular hubs are as usefulin the PSN context as they are in the wireline Internet and inthe Web.

We also provide details of the statistics of interactions in the ex-periments so that they can be used by other researchers in futuremodeling, or to bootstrap larger experiments consisting of compos-ites of these.

In the second half of this paper we look at how can we use this in-formation to make smart forwarding decisions. The following threepre-existing schemes provide lower and upper bounds in terms ofcost and delivery success. All of these schemes are inefficient be-cause they assume a homogeneous environment. If the environmentis homogeneous then every node is statistically equivalent, and ev-ery node has the same likelihood of delivering the messages to thedestination. As we showed in the first half of this paper, the envi-ronments and nodes are diverse, and hence all these naive schemesare doomed to have poor performance. We need to design algo-rithms which make use of this rich heterogeneity.

WAIT Hold on to a message until the sender encounters the recip-ient directly. Cheap, but unbounded expected mean delay.

FLOOD Messages are flooded throughout the entire system.

MCP Multiple-Copy-Multiple-Hop.Multiple Copies are sent sub-ject to a time-to-live hop count limit on the propagation ofmessages. By exhausted emulations, 4-copy-4-hop MCP schemeis found to be most cost effective scheme in term of deliveryratio and cost for all naive schemes among all the datasetsexcept the HK data. Hence for fair comparison, we wouldlike to evaluate our algorithms against the 4-copy-4-hop MCPscheme in most of the cases.

The Mobile network has a dual nature: it is both a physical net-work and at the same time it is also a social network. A node inthe network is a mobile device, and also associated with a mobilehuman.

Figure 10 shows the design space for the forwarding algorithmsin this paper. The vertical axis represents the explicit social struc-ture, that is facets of nodes that can specifically identified such asaffiliation, organization or other social context. This is the socialor human dimension. The two horizontal axes represent the net-work structural plane, which can be inferred purely from observedcontact patterns. The Structure-in-Cohesive Group axis indicatesthe use of localized cohesive structure, and the Structure-in-Degreeaxis indicates the use of hub structure. These are observable phys-ical characteristics. In our design framework, is not necessary thatphysical dimensions are orthogonal to the social dimension, butsince they are represent two different design parameters, we wouldlike to separate them. The design philosophy here is to include boththe social and physical aspects of mobility into considerations.

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Explicit Social Structure

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Figure 10: Design space for forwarding algorithms.

LABEL Explicit labels are used to identify forwarding nodes thatbelong to the same organization. Optimizations are exam-ined by comparing label of the potential relay nodes and thelabel of the destination node.This is in the human dimension,although an analogous version can be done by labelling a k-clique community in the physical domain.

RANK This is analogous to the degree of a node in a fixed network;we use a modified ranking scheme, namely the node central-ity in a temporal network. It is based on observations in thenetwork plane, although it also reflects the hub popularity inthe human dimension.

DEGREE A heuristic based on the observed average of the degreeof a node over some longer interval. Either the last intervalwindow (S-Window), or a long term accumulative estimate,(A-Window)) is used to provide a fully decentralized approx-imation for each node’s centrality, and then that is used toselect forwarding nodes.

BUBBLE The Bubble family of protocols combines the observedhierarchy of centrality of nodes with explicit labels, to de-cide on the best forwarding nodes. Bubble is an examplealgorithm which uses information from both the human as-pects and also the physically observable aspects of mobility.

In the following sections, we will show how can we make useof these different metrics to improve forwarding performance in aheterogeneous system and also when they will fail. We focus onempirical analysis; that is what our mobile network research com-munities most lack; we do not consider abstracting a mathematicalmodel in this work, but evaluate the forwarding schemes directlyon the mobility traces.

7. GREEDY RANKING ALGORITHMThe third contribution of this paper is to modify the greedy rank-

ing search scheme over power law networks to apply to our tempo-ral graphs, and evaluate the resulting algorithm.

7.1 The Power of Greedy RankingHere we use a similar greedy strategy to the one Adamic et al.

introduced in [1]. A PSN is not like Internet: we do not know when

a global or local maximum is reached since the next encounter isunexpected. We cannot employ precisely the same strategy as theypropose, of traversing up the hierarchy until reaching the maxi-mum, and then down a step. Here we also assume each node knowsonly its own ranking and the rankings of those it encounters, butdoes not know the ranking of other nodes it does not encounter, anddoes not even know which node has the highest rank in the system.Our strategy, which we call RANK, is very simple: we keep push-ing traffic on all paths to nodes which have a higher ranking thanthe current node, until either the destinations are reached, or themessages expire.

If a system is small enough, the global ranking of each node isactually the local ranking. If we consider only the Rummidge Com-puter Laboratory System Research group, this is the the ranking ofeach node inside the group. If we consider the whole ComputerLaboratory, we are considering a larger system of many groups,but they all still use the same building. A homogeneous rankingcan also work. But when we consider the whole city of Rum-midge, a homogeneous ranking would exclude many small scalestructures. In this section we show that in relative small and homo-geneous systems, a simple greedy ranking algorithm can achievegood performance.

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Figure 11: Comparison of delivery ratio (left) and cost(right) ofMCP and greedy RANK on 4 copies and 4 hops case (Reality).

Figure 11(a) shows that the simple greedy ranking perform al-most as well as MCP for delivery. Figure 11(b) also shows that thecost is only around 40% that of MCP, which represents a markedimprovement.

Hierarchical organization is a common feature of many complexsystems. The defining feature of a hierarchical organization is theexistence of a hierarchical path connecting any two of its nodes.Trusina et al. [23] address how to detect and measure the extent ofthe hierarchy manifested in the topology of a given complex net-work. They defined the hierarchical path based on node degrees,a path between two nodes in a network is called hierarchical if itconsists of an “up path” where one is allowed to step from node i

to node j only if their degrees ki, kj satisfy kiu ≤ kj , followed bya “down path” where only steps to nodes of lower or equal degreeare allowed. Either the up or down path is allowed to have zerolength. Because of the good achievement from the greedy rankingalgorithm, we are going to analyse the percentage of hierarchicalpaths inside all the shortest paths. Table 3 summarises the results.

The percentage of hierarchical paths is calculated as the numberof hierarchical paths divided by the number of non-direct transferdeliveries. We can see that for Rummidge data and Reality Mining,the percentage of hierarchical paths is very high, so our strategy ofpushing the messages up the ranking tree can probably find a lotof these paths, and the performance of the ranking strategy here isnot much different from the MCP. For Infocom06 and Infocom05,the percentages of hierarchical paths is also high, so the greedy

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Experimental data set % hierarchical pathsRummidge 87.2 (-2.4,+4.3)

Reality 81.9 (-3.1,+3.3)Infocom05 62.3 (-2.5,+2.5)Infocom06 69.5 (-4.1,+2.4)Hong Kong 33.5 (-4.0,+4.0)

Table 3: Hierarchical Paths analysis of all shortest paths

RANK strategy can also discover many of the shortest paths. How-ever, for Hong Kong experiment, the network is too sparse and alot of shortest paths are hidden, because we could not know thedevices detected by the external devices, and most of the resultingpaths used for delivery are actually not the shortest . We can seethat percentage of hierarchical paths controls the delivery successthat is achieved by the greedy RANK algorithm. We conclude fromthis that a very high percentage of the shortest paths are actuallyhierarchical paths.

7.2 Where the Greedy Ranking FailsFor the Hong Kong dataset, the 37 participants are intentionally

selected without any social correlation. They live and work dis-tributively throughout the whole city. Relying on direct contact,less than 4% of the messages can be delivered. Unlike all the previ-ous datasets, here all the external Bluetooth devices detected needto be used for constructing the paths. But because we don’t knowthe devices detected by all these external devices so a lot of poten-tial paths not found.

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Figure 12: Comparison of delivery ratio and cost of MCP andGreedy RANK on no constraints case (HK)

Figure 12(a) and Figure 12(b) show the delivery ratio and deliv-ery cost using flooding, and using unlimited greedy ranking. Wecan see that using flooding, we can deliver more than 40% of thetotal traffic across the whole city by using only the 37 iMotes andthe external devices detected by these iMotes without knowing thedevices detected by the external devices, that will be a huge num-ber of paths out of these 869 devices. However the cost is also veryhigh: to deliver one message, we need to make around 180 copies.But in this case, greedy ranking can only deliver 10% of the mes-sages, although the cost is much lower as well. In terms of deliveryand cost, greedy ranking is still more cost-effective than flooding,but clearly the delivery success rate is still too low. One explana-tion for this low performance is that since the participants have nosocial correlation, and belong to different social communities, highglobal ranking of a node may not represent a good choice of re-lay for some local communities. Messages keep being pushed upto some globally higher ranking nodes, and getting stuck at some

maxima, rather than then trickling down to some local community.Figure 13(a) shows that the maximum number of hops for greedyRank is 4 hops and after that the messages get stuck. Figure 13(b)shows the rank distribution of the source, destination and dead-endof all the undelivered messages, we can see that these “dead-endnodes” have relatively high ranking, and this supports our hypoth-esis concerning messages stuck at maxima.

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Figure 13: The hop distribution of the delivered(left) and therank distribution of undelivered(right) on HK data.

8. DIRECT LABELLING STRATEGYIn the “labelling strategy” [11], each node is assumed to have

a label that tells others its affiliation, just like a name badge in aconference. The “direct labelling strategy” refers to the exclusiveof labels to forward messages to destinations: next-hop nodes areselected if they belong to the same group (same label) as the desti-nation. Our fourth contribution is to evaluate the improvements toforwarding possible using this a priori affiliation label data.

8.1 The Power of LabellingThe direct labelling strategy is evaluated on the Infocom06 data.

Since this is a conference scenario, where people meet frequently,direct labelling strategy works quite well as we might expect. InFigure 14(a) we see that, as expected, LABEL has a delivery ratiobetween MCP and WAIT, and the trend is for it to approach closerto the performance of MCP, as we increase the lifetime (TTL) ofmessage. In terms of cost, in Figure 14(b) we can see that MCPcosts much more than LABEL, especially when TTL is increased to1 day, where MCP has less than a 10% improvement over LABEL,but has around 6 times the cost. Of course, WAIT has the lowestcost: since we are in a conference scenario, we do not expect towait long to meet the destination, hence the delivery ratio is not toolow.

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Figure 14: Comparison of delivery ratio and cost of MCP andLABEL on 4 copies and 4 hops case (Infocom06)

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8.2 The Problem with Direct LabelingA human community represents one type of long term, stable re-

lationship. An outside observer of human society would not knowat first to which group each person belongs. As time goes by,we gain higher confidence concerning who usually socialises withwhom. In this part of analysis, we use the communities detectedfrom the 9 month Reality Mining traces. Nine months is a longenough period for us to have high confidence to believe that thecommunities extracted from the dataset truly reflect the social com-munities existing between the participants. We think it is accurate,then, to evaluate the labelling strategy on this dataset.

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Figure 15: Comparison of delivery ratio(left) and cost(right) ofMCP and LABEL on 4 copies and 4 hops case (Reality).

We can see from Figure 15 that “labelling strategy” only achievesaround 55% of the delivery ratio of the MCP strategy and only 45%of the flooding delivery although the cost is also much lower. How-ever it is not an ideal scenario for LABEL. In this environment, peo-ple do not mix as well as in a conference. A person in one groupmay not meet members in another group so often, so waiting untilthe member of the another group appear to do the transmission isnot effective here.

Figure 16 shows the correlation of the nth-hop relay nodes to thesource and destination groups for the messages on all the shortestpaths, that is the percentage of the nth-hop relay nodes that are stillin the same group as the source or already in the same group as thedestination. We can see that more than 50% of the nodes on thefirst hops (from the S-Group plot) are still in the same group as thesource group of the message and only around 5% of the first hopnodes (from the D-Group plot) are in the same group as the des-tination. This explains why direct labelling is not effective, sinceit is far from discovering the shortest path. We can also see thaton going to the 2nd hop, S-Group correlation drops to slightly lessthan 30%, and when going to 4th-hops, almost all (90%) messageshave escaped from this source group. To calculate the percentagefor each hop we just divide the count of messages which belongto that group by the total count of messages destined beyond thatnode, but not the total messages created. In the 4-hop case, thereare perhaps only 100 messages to forward further, and only 10 outof these 100 relay nodes belong to the source group.

9. CENTRALITY MEETS COMMUNITYThe fifth contribution in this paper is to combine the knowl-

edge of both the centrality of nodes and the community structure,to achieve further performance improvements in forwarding. Weshow that this avoid the occurrence of the dead-ends encounteredwith pure global ranking schemes. We call the protocols here BUB-BLE, to capture our intuition about the social structure. Messagesbubble up and down the social hierarchy, based on the observedcommunity structure and node centrality, together with explicit la-

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bel data. Bubbles represent a hybrid of social and physically ob-servable heterogeneity of mobility over time and over community,and contrast with the notion of a pocket, which is a DTN area ofcurrent wireless reachability.

9.1 Two-community CaseIn order to make the study more systematic, we start with the

two-community case. We use the Rummidge dataset for this study.By experimental design, and confirmed using our community de-tection algorithm, we can clearly divide the Rummidge data intotwo communities: the undergraduate year1 and year2 group. Inorder to make the experiment more fair, we limit ourselves to justthe two 10-clique groups found with a number-of-contact threshold29; that is where each node at least meet another 9 nodes frequently.Some students may skip lectures and cause variations in the results,so this limitation makes our analysis yet more plausible.

First we look at the simplest case, for the centrality of nodeswithin each group. In this case, the traffic is created only for mem-bers within the same community and only members in the samecommunity are chosen as relays for messages. We can see clearly

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Figure 17: Node centrality in 2 groups in Rummidge datafrom Figure 17(a) and 17(b) that inside a community, the centralityof each node is different. In Group B, there are two nodes which arevery popular, and relayed most of the traffic. All the other nodeshave very low centrality value. Forwarding messages to the pop-ular nodes would make delivery more cost effective for messageswithin the same community.

Then we consider traffic which is created within each group andonly destined for members in another group. To eliminate otheroutside factors, we use only members from these two groups as re-lays. Figure 18(a) shows the individual node centrality when traffic

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is created from one group to another. Figure 18(b) shows the corre-lation of node centrality within an individual group and inter-groupcentrality. We can see that points lie more or less around the diago-nal line. This means that the inter- and intra- group centralities arequite well correlated. Active nodes in a group are also active nodesfor inter-group communication. There are some points on the lefthand side of the graph which have very low intra-group centralitybut moderate inter-group centrality. These are nodes which moveacross groups. They are not important for intra-group communica-tion but can perform certainly well when we need to move trafficfrom one group to another.

We can show now why homogeneous global ranking in section 7does not work perfectly. Figure 19 shows the correlation of the

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local centrality of Group A and the global centrality of the wholepopulation. We can see that quite a number of nodes from GroupA lie along the diagonal line. In this case the global ranking canhelp to push the traffic toward Group A. However the problem isthat some nodes which have very high global rankings are actuallynot members of Group A, for example node D. Just as in real soci-ety, a politician could be very popular in the city of Rummidge, butnot a member of the Computer Laboratory, so would not be a verygood relay to deliver message to the member in the Computer Lab-oratory. Now we assume there is a message at node A to deliverto another member of Group A. According to global ranking, wewould tend to push the traffic toward B, C, D, and E in the graph. Ifwe pushed the traffic to node C, it would be fine, to node B wouldbe perfect. But if it push the traffic to node D and E, the traffic

could get stuck there and not route back to Group A. If it reachesnode B, that is the best relay for traffic within the group, but nodeD has a higher global ranking than B, and would tend to forwardthe traffic to node D, where it would probably get stuck again.

Hence we now propose the following forwarding algorithm 1 toavoid these dead-ends:

Algorithm 1: BUBBLE RAPbegin

var use GlobalRanking ← true

if (Label(currentNode) == Label(destination)) thenuseGlobalRanking ← false

foreach EncounterNode i doif Rank(nodei) > Rank(currentNode) or Label(nodei) ==Label(destination) then

Buffer(node i)← Buffer(node i)S

{message}

end

If a node has a message destined for another node, this nodewould first bubble this message up the hierarchical ranking tree us-ing the global ranking until it reaches a node which has the samelabel(community) as the destination of this message. Then the localranking system will be used instead of the global ranking and con-tinue to bubble up the message through the local ranking tree untilthe destination is reached or the message expired. This methoddoes not require every node to know the ranking of all other nodesin the system, but just to be able to compare ranking with the nodeencountered, and to push the message using a greedy approach. Wecall this algorithm Bubble-A, since each world/community is likea bubble. Figure 20 illustrates the algorithm. A global bubble isalways relative to local bubble. This global bubble maybe a sub-bubble of another larger bubble.

Ranking

Source

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Sub community

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Figure 20: Illustration of the bubble forwarding algorithm.

This fits our intuition in terms of real life. First you try to forwardthe data via people more popular than you around you, and thenbubble it up to well-known popular people in the society, such asa postman. When the postman meets a member of the destinationcommunity, the message will be passed to that community. Thiscommunity member will try to identify the more popular memberswithin the community and bubble the message up again within thelocal hierarchy until the message reach a very popular member, orthe destination itself, or the message expires.

A modified version of this strategy is that whenever a messageis delivered to the community, the original carrier can delete thismessage from its buffer to prevent it from further dissemination.This assumes that the community member would be able to deliver

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this message. We call this protocol with deletion, strategy Bubble-B.

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Figure 21: Comparisons of several algorithms on Rummidgedataset, delivery(left) and cost(right).

We can see from Figure 21(a) that both Bubble-A and Bubble-B achieve almost the same delivery success rate as the 4-copy-4-hop MCP. Although Bubble-B has the messages deletion mecha-nism, it achieves exactly the same delivery as Bubble-A. From Fig-ure 21(b), we can see that Bubble-A only has 60% the cost of MCPand Bubble-B is even better, with only 45% the cost of MCP. Bothhave almost the same delivery success as MCP.

9.2 Multiple-community CasesTo study the multiple-community cases, we use the Reality Min-

ing dataset as in section 8.2.To evaluate the forwarding algorithm, we extract a 3 week ses-

sion during term time from the whole 9 month data set. Emulationsare run over this dataset with uniformly generated traffic.

There is a total 8 groups within the whole dataset. Figure 22shows the node centrality in 4 groups, from very small size tomedium size and large size group. We can see that within eachgroup, almost every node has different centrality.

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Figure 22: Node centrality in several individual groups in Re-ality Mining.

In order to make our study easier, we first isolate just one group,the largest one in Figure 22, consisting of 16 nodes. In this case,all the nodes in the system create traffic for members of this group.We can see from Figure 23(a) that Bubble-A and Bubble-B per-form very similarly to MCP most of the time in the single groupcase, and even outperform MCP when the time TTL is set to be

larger than 1 week. From Figure 23(b), we can see that Bubble-A only has 70% and Bubble-B only 55% of the cost of MCP. Wecan say that the Bubble algorithms are much more cost effectivethan MCP, with high delivery ratio and low delivery cost. After thesingle group case, we start looking at the case of every group creat-ing traffic for other groups, but not for its own members. We wantto find the upper cost bound for the Bubble algorithm, so we donot consider local ranking; messages can now be sent to all mem-bers in the group. This is exactly a combination of direct LABELand greedy RANK, using greedy RANK to move the messages awayfrom the source group. We do not implement the mechanism to re-move the original message after it has been delivered to the groupmember, so the cost here will represent an upper bound for Bubbletype algorithms.

From Figure 23(c) and Figure 23(d), we can see that of courseflooding achieves the best performance for delivery ratio, but thecost is 2.5 times that of MCP, and 5 times that Bubble. Bubbleis very close in performance to MCP in multiple groups case aswell, and even outperforms it when the time TTL of the messagesis allowed to be larger than 2 weeks. However, the cost is only 50%that of MCP.

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Figure 23: Comparisons of several algorithms on Reality Min-ing dataset, single group and all groups.

10. MAKING CENTRALITY PRACTICALHow can each node know its own centrality in a decentralised

way? How well does past centrality predict the future.The final contribution of this paper is to provide early answers to

these two questions.

10.1 Approximating centralityWe found that the total degree (unique nodes) seen by a node

throughout the experiment period is not a good approximation forthe node centrality. Instead the degrees per unit time (for examplethe number of unique nodes seen per 6 hours) and the node central-ity has a high correlation value.

We can see from Figure 24 that some nodes with a very hightotal degree are still not good carriers. It also shows that the per6 hour degree is quite well correlated to the centrality value, withcorrelation coefficient as high as 0.9511. The means that how many

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H

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HML

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Figure 24: Correlation of rank with total degree and rank withunit time degree (Reality).

people you know doesn’t matter too much, but how frequently youinteract with these people matters.

In order to verify that the average unit-time degree is as good asor close to RANK, we run another sets of emulations using greedyaverage unit-time degree(or we simply call it DEGREE) instead ofthe pre-calculated centrality. Figure 25(a) and Figure 25(b) com-

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Figure 25: Comparisons of delivery(left) and cost(right) ofRANK and DEGREE on Reality Mining dataset, all groups.

pare the delivery ratio and delivery cost of using greedy RANK andgreedy DEGREE. We can see that RANK and DEGREE perform al-most the same with the delivery and cost lines overlapping eachother. They not only have similar delivery but also similar cost.

However, the average unit-time degree calculated throughout thewhole experimental period is still difficult for each node to calcu-late individually. We then consider the degree for previous unit-time slot( we call this the slot window) such that when two nodesmeet each other, they compare how many unique nodes they havemet in the previous unit-time slot (e.g. 6 hours). We call thisapproach the single window (S-Window). Another approach isto calculate the average value on all previous windows, such asfrom yesterday to now, then calculate the average degree for ev-ery 6 hours. We call this approach the accumulative window (A-Window). This technique is similar to a statistics technique calledexponential smoothing [25] and we would like to do further theo-retical investigation.

The S-Window approach reflects more recent context and achievesmaximum of 4% improvement in delivery ratio than DEGREE, butat double the cost. The A-Window approach measures more of theaccumulative effect, and gives more stable statistics about the aver-age activeness of a node. However, its accumulative measurementis not as good an estimate as DEGREE, which averages throughoutthe whole experimental period. It does not achieve as good deliveryas DEGREE (not more than 10% less in term of delivery), but it alsohas lower cost.

All these approaches, (DEGREE, S-Window and A-Window) canprovide us with a decentralised way to approximate the centralityof nodes in the system, and hence help us to design appropriate

forwarding algorithms.

10.2 Predictability of Human MobilityWe now try to verify whether the centrality measured in the past

is useful as a predictor for the future. As well as the subset ofthe data we used in section 9.2, we extracted another two 3-weeksessions from the dataset. We then run a set of greedy RANK emu-lations on these, but using the centrality values from section 9.2.

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Figure 26: Delivery ratio(left) and cost(right) of RANK algo-rithm on 2nd data session, all groups (Reality)

Figure 26(a),(b) show the delivery ratio and cost of RANK onthe 2nd data session using the centrality values from the 1st datasession. It seems that the performance of RANK is not far fromMCP but with much lower cost. The performance is as good as inthe original dataset. Similar performance is also observed in the3rd data session. These results imply some level of human mo-bility predictability, and show empirically that past contact infor-mation can be used in the future. Further investigation on humanpredictability will be done by using graph similarity [2] and alsoother statistical techniques.

11. RELATED WORKNewman et al. used betweenness [17] and modularity [16] to

detect community structure in complex networks. The between-ness of an edge is defined as the number of shortest paths betweenvertex pairs that run along it, summed over all vertex pairs. Theycalculate the betweenness of all edges in the network, remove theone with highest betweenness, and repeat the process until no edgeremain. They also introduce a measure called modularity to evalu-ate how good a particular division is. This measures the fraction ofedges that are within the same community, less the expected valueof the same quantity in a network with the same community divi-sion but random connection between the vertices. The differencebetween this algorithm and k-clique is that the k-clique approachallows overlapping community to exist, but the Newman methoddivides nodes into completely disjoint communities. This is thereason that we choose k-clique in our work. We have also im-plemented the Newman algorithm for a weighted network but forspace reasons this is left to be reported in other work.

For distributed search for nodes and content in power law net-works, Sarshar et al. [22] proposed using a probabilistic broadcastapproach: sending out a query message to an edge with probabil-ity just above the bond percolation threshold of the network. Theyshow that if each node caches its directory via a short random walk,then the total number of accessible contents exhibits a first-orderphase transition, ensuring very high hit rates just above the perco-lation threshold.

12. CONCLUSION AND FUTURE WORK

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Networks exhibit power law node degree distributions, and scale-free networks appear to be an important model for graphs whichevolve through preferential attachment and re-wiring. In this pa-per, we extend this modelling to mobile ad hoc and delay tolerantnetworks through experimental study of PSNs. We use this workto confirm the original conjecture that the use of social preferentialattachment is a good heuristic for forwarding algorithms for tem-poral graphs in a number of ways, whether by a priori labels orthrough use of social structures inferred through observation.

A k-clique community can be built up by distributed gossip-ping [13]. For a complete analysis of gossipping in PSN, we modela PSN as a temporal graph with edges between two nodes thatcome and go following a power law distribution with certain co-efficient. The power law model for edges is based on prior mea-surement work reported in [4] and [10]. We would like to considerseveral network topologies for degree attachment including simpleplane lattice [13], Erdos-Renyi random graph, scale-free networkand also the mobility traces we have.

Other forwarding algorithms [?] [?] have and will be devised forDTNs, and should be evaluated in the context of the mobility andsocial models we have described here. Use of additional resourcessuch as geographic location data, and of infrastructural nodes toassist in forwarding must be invstigated.

In section 10.1 we chose 6 hours from the intuition that daily lifeis divided into 4 main periods, morning, afternoon, evening andnight, each almost 6 hours. This appears to work, however, futurework will look at how sensitive the system is to the choice of thisperiod.

Current k-clique algorithm only support binary graphs, a weightedversion should be targeted to eliminate the manual involvement ofchoosing the weight thresholds.

Further experimental work involving larger scale experiments isrequired to confirm our results with more confidence in a wider va-riety of settings. Furthermore, we believe that it should be possibleto abstract mathematical models of mobility that match our empiri-cal results that can be used to generate further data sets with whichto evaluate our and other forwarding systems.

We believe that this paper represents a first step in combiningrich multi-level information about social structures and interactionsto drive novel and effective means for disseminating data in DTNs.A great deal of future research can follow.

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