Snapshot: a forwarding strategy based on analyzing networktopology in opportunistic networks

Junyeop Lee • Sun-Kyum Kim • Ji-Hyeun Yoon •

Sung-Bong Yang

Published online: 29 January 2015

� Springer Science+Business Media New York 2015

Abstract We study a forwarding strategy in opportunistic

networks which are one of the most challenging networks

among mobile ad-hoc networks. In opportunistic networks,

a node does not have knowledge about the entire network

topology, which is essential in the mobile ad-hoc network’s

forwarding strategy. Thus, node behavior is exploited to

calculate future contact opportunities for forwarding a

message. Utilizing social network analysis (e.g., similarity

and centrality) has been proposed to improve the accuracy

of the calculation task. This paper proposes a forwarding

strategy based on an analysis of network topology. In the

proposed strategy, each node takes a sequence of snapshots

of its first-order neighbors during a warm-up period. Each

node exchanges its own snapshots with each other, and

then aggregates the snapshots in order to extract the net-

work topology information. The extracted network topol-

ogy is analyzed by social network analysis methods:

compactness and algebraic connectivity. Forwarding

decisions are made using the analysis of the features

(compactness and algebraic connectivity). We present

simulations using NS-2 and the home-cell community-

based mobility model to show that the proposed forwarding

strategy results in delay performances similar to the epi-

demic forwarding scheme, while maintaining reasonable

network traffic. In addition, we demonstrate that the pro-

posed strategy outperforms the SimBet and PRoPHET

forwarding schemes with various communication ranges

and memory space.

Keywords Opportunistic networks � Social networks

analysis � Forwarding � Network topology

1 Introduction

In recent years, research on ad hoc networks has focused on

the challenges of new network paradigm instead of the

traditional ‘client–server’ network system, because main-

taining the traditional system requires high maintenance

costs. In addition, it is difficult to build and maintain the

traditional system in some tough environments, such as

battlefields, in places with no electricity, the deep sea, and

the outer-space [10, 20, 28]. Hence, it is necessary to

develop a cost effective and easily applicable network

system. An opportunistic network system as a new alter-

native solution is one of the most challenging networks in

which there are non-stable forwarding paths and intermit-

tent connections [6, 7].

One of the main topics of research on opportunistic

networks is the development of a feasible forwarding

scheme, because finding paths towards the destination is

not a trivial matter due to a lack in topological network

information [27]. If a forwarding scheme is able to obtain

the estimated network topology information, its forwarding

performance may improve considerably. However, there

are tradeoffs and limitations to obtaining such topological

information.

The forwarding strategies in opportunistic networks

without infrastructure can be classified into two types [27]:

J. Lee � S.-K. Kim � J.-H. Yoon � S.-B. Yang (&)

Department of Computer Science, Yonsei University, Seoul,

Korea

e-mail: sbyang@cs.yonsei.ac.kr

J. Lee

e-mail: kotzyi@yonsei.ac.kr

S.-K. Kim

e-mail: skyum@yonsei.ac.kr

J.-H. Yoon

e-mail: y_chick@yonsei.ac.kr

123

Wireless Netw (2015) 21:2055–2068

DOI 10.1007/s11276-015-0900-9

the context-based scheme and the dissemination-based

scheme. In the context-based scheme, each node utilizes

the contexts of the nodes to determine the best relay nodes.

Thus, the context-based scheme reduces unnecessary net-

work traffic. Typical context-based schemes have been

proposed in [1, 15, 17, 22, 24, 30]. However, the context

scheme should overcome the privacy issue to obtain indi-

vidual context information. In addition, it’s necessary for

the schemes to update the context information since the

network environment and the context information of the

nodes change dynamically. On the other hand, in the dis-

semination-based scheme, each node disseminates the

message all over the network because each node hardly

knows a route towards either the destination or the best

next hop [33]. There are two drawbacks in the dissemina-

tion-based scheme. One is that each node does not have

enough memory space to keep the messages to be for-

warded due to the limitation of the memory size. Espe-

cially, nowadays, when much of the memory space is

consumed by large size messages, such as videos or photos.

The other drawback is that traffic congestion may not be

avoided since all the messages are forwarded without any

consideration to the reduction of traffic. To control the

network congestion, various schemes have been proposed

[4, 8, 14, 23, 35]. Most of these schemes use some local

information such as relationships or similarities among the

nodes in the network. However, they may suffer from

much longer transmission delays. We assume that each

node cannot completely access other nodes’ context

information due to privacy issues. Thus, we focus on

developing a dissemination-based scheme.

In this paper, we propose a forwarding scheme that

overcomes the aforementioned drawbacks. The proposed

scheme is called Snapshot; it begins by periodically col-

lecting the global information, such as the network topol-

ogy. Each node accumulates and shares the contact

information in order to obtain the network topology

information, because an opportunistic network can be

viewed as a distributed network system. Note that the

accumulated and shared information may depict a partial

network topology. Each node analyzes the respective

topological information with the social network analysis

methods, and then extracts some topological features from

the analyzed information. Simulations with NS-2 [25] to

compare the epidemic [33], PRoPHET [23] and SimBet [8]

schemes were performed, showing that Snapshot is supe-

rior in terms of both the transmission delay time and net-

work traffic. The simulation results also show that the

network topology obtained during each time period is fairly

accurate and that the extracted topological features have

been applied properly for a better performance.

The technical contributions of this paper can be sum-

marized as follows.

• A novel scheme known as Snapshot is devised to obtain

network topology in each time period: most forwarding

schemes focus on how to exploit the local information.

However, in the proposed scheme, we extract some

essential information from the network topology to

control all the nodes as a whole in the network.

• Network topology is periodically considered: the pro-

posed scheme keeps all the observed topological

information at specific times in order to dynamically

obtain the network features. Hence, the proposed

scheme is able to adapt to any opportunistic network

environment and control the network accordingly.

• The social network concept is applied to a forwarding

scheme: most forwarding schemes focus on utilizing

features of the nodes. However, we use two features

that are used in social network analysis: the compact-

ness of a connected component and the algebraic

connectivity.

The rest of the paper is organized as follows. Section 2

explains the related work, and Sect. 3 describes how the

proposed scheme works in detail. In Sect. 4, we present the

simulation results. Finally, we conclude the paper in Sect.

5.

2 Related work

2.1 Classification of forwarding schemes

in opportunistic networks

The forwarding schemes in opportunistic networks can be

classified into two groups: dissemination-based schemes

and context-based schemes. Dissemination-based schemes

are basically to manipulate flooding. Context-based

schemes utilize the knowledge of nodes in order to deter-

mine the best next hop.

In the dissemination-based schemes, each node diffuses

a message all over the network because the schemes may

not have comprehensive knowledge about stable paths

towards either the destination or the best next hop. A

message will finally be delivered to the destination by

relaying the message. The dissemination-based schemes

clearly perform well in terms of delay time, because there

are plenty of contact opportunities among the nodes.

However, they suffer from too much network traffic due to

too many relayed messages. On the other hand, the context-

based schemes utilize the context information of the nodes

to find proper relay nodes that deliver the message to the

destination. Thus they significantly reduce duplicate mes-

sages. However, they are subject to a longer transmission

delay, because they may not choose appropriate relay

nodes all of the time. In order to determine appropriate

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123

relay nodes, the context-based schemes usually require a

more intensive computation process than the dissemina-

tion-based schemes. In addition, the context-based schemes

should update the context information of the nodes since

the network environment changes dynamically.

2.2 Dissemination-based forwarding schemes

The epidemic forwarding scheme [33] spreads the mes-

sages all over the network like the epidemic spread of

viruses. Once a node receives a message, it keeps the

message in its memory space and sends the message to

other nodes encountered. However, the dissemination

procedure may be impeded by a limited hop count [time to

live (TTL)]. If the hop count limit is one, the delivery

process cannot be accomplished except for when the sender

node encounters the destination. Our proposed scheme

partially adopts the basic strategies of the epidemic

scheme, but our scheme determines a proper TTL length

with the network topological information.

The PRoPHET forwarding scheme [23] allows each node

to collect the contact patterns of other nodes. Each node

computes the predictability that a node delivers the message

to the destination. Two nodes then exchange the summary

vectors when they encounter each other, including the

delivery predictability information with respect to the des-

tination. Afterwards, each node determines the next best hop

from the summary vector information. Our proposed scheme

utilizes the contact patterns to obtain the network topology.

The two-hop multi-copy scheme [13, 14] lets the source

node keep sending the message to all the encountered nodes.

Only a node that receives the message from the sender keeps

a copy of the message. The nodes with the message copies

send the messages to other nodes whenever possible. This

process may drastically reduce network traffic due to con-

fining of the number of nodes that carry the messages. Our

proposed scheme maintains a proper number of nodes (called

messengers) that carry the messages, but the number of

messengers is determined by the network topology.

The SimBet forwarding scheme [8] utilizes the social

information. When two nodes meet, they exchange infor-

mation about data messages along with the list of neigh-

bors. Each node then determines the ‘betweeness’ and

‘similarity’ values from the information. The betweeness

value of a node is the number of shortest paths from all

nodes to all others that pass through the node. The simi-

larity value is the number of common neighbors between

two nodes. The betweeness and similarity values are used

to predict which node is the best next hop. Our scheme also

utilizes some structural properties used in the social net-

work analysis in order to acquire essential features such as

algebraic connectivity, compactness, and the number of

components.

2.3 Context-based forwarding schemes

The context-aware routing protocol [24] lets each node

compute the delivery probabilities for all the destination

nodes. Each node then determines the best carrier based on

the nodes’ context such as the current battery level or the

degree of mobility. The best carrier then saves the message,

and forwards it to the destination or a node with higher

probability.

In the MobySpace forwarding scheme [22], each node

uses mobility patterns as the context information. Moby-

Space is defined as a multi-dimensional Euclidean space

where each axis denotes a possible contact between two

nodes, and the distance is the contact probability. If two

nodes are close to each other in the MobySpace, they may

have similar contact patterns. Thus the best carrier is

chosen as the node that is closest to the destination in the

MobySpace. In order to construct a more precise Moby-

Space, the contexts of all the nodes are required.

3 Proposed scheme

3.1 Overview

Most forwarding schemes exploit the user similarity or

contact information of the nodes in a network. These for-

warding schemes could reduce network traffic, while they

could not avoid a longer transmission delay. Thus, we

propose a novel forwarding scheme to resolve such a

problem. In our proposed scheme, each node takes ‘snap-

shots’ of the network during the warm-up period and

extracts important topological information from the snap-

shots as well as the period a message is forwarded.

By ‘taking snapshots’ we mean that each node periodi-

cally collects the information of the first-order neighbors

during the warm-up period. Note that a node also

exchanges its snapshots with its first-order neighbors to

update its own topological information. At the end of the

warm-up period, each node extracts (1) the change period

of the membership in the connected component [a con-

nected component (or just the component) in an undirected

graph is a maximal connected subgraph], (2) the com-

pactness of each component, and (3) the number of con-

nected components from the topological information. Next

we will describe the proposed scheme in detail.

3.2 The proposed scheme

The proposed scheme consists of three steps.

Step 1: Each node takes a snapshot in a regular time

interval during the warm-up period; that is, each node

Wireless Netw (2015) 21:2055–2068 2057

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collects the IDs of its first-order neighbors and records time

ts, where s = 1,…,w, when the receptions occur. Note that

the time of the receptions from its neighbors is assumed to

be identical while taking a snapshot. We assume that each

node in the network knows the wall-clock time and each

snapshot in a node has a time stamp that shows the time it

was taken. Therefore, when a node encounters another

node, they swap their own snapshots each other. Each node

merges its snapshots with the snapshots received according

to the time stamps. For example, if there are w snapshots

taken at times t1, t2,…, tw each, then both encountered

nodes have the same copies of w snapshots after merging.

Observe that as time passes each snapshot at ts of a node is

reinforced as if we keep finding ‘‘the missing puzzle pie-

ces’’ to try to achieve the entire network topology at time

ts. Hence the proposed scheme doesn’t need any special

mechanism for synchronization for taking snapshots among

the nodes. Table 1 shows sample snapshot information for

nodes.

The snapshot information is also exchanged between

the nodes in the warm-up period. The purpose of

exchanging the snapshot information is to construct a

network topology at ts. Note that since the network is

constructed based on the snapshots of the node and the

snapshots gathered from the neighbors, it may be a

partial network. With the snapshot information of all the

nodes in the network we can construct the entire topol-

ogy of the network at ts because the accumulated snap-

shot information includes all the connections among all

nodes in the network at that time.

Figure 1 illustrates the snapshots (adjacency matrices)

of n1 before and after exchanging the snapshot information

with n2. At time t1, node n1 encounters nodes n2, n3, and n4.

At the same time, n2 encounters n1, n4, and n5, as shown in

Fig. 1a. Figure 1b shows the snapshot information of both

n1 and n2. Figure 1c, d show the adjacency matrices of n1

before and after exchanging the snapshot information,

respectively.

Step 2: A node extracts three network features from the

adjacency matrix: (1) the change period of membership in

the component, (2) the compactness of each component

and (3) the number of components.

1. The change period of membership in the component

is used to determine the ‘pumping’ period. By

pumping we mean that a node that has the message

in its memory sends it to its neighbors and each

(relay) node that receives the message also imme-

diately sends it to its neighbors. Note that a relay

node does not keep the message in its memory, in

order to have a tolerance towards memory size. To

find the appropriate pumping period for node ni, we

measure what fraction of the nodes in the compo-

nent to which ni belongs has changed. Node nipumps the message only when a certain percentage

of the members in the component have changed.

This pumping contributes to reducing the network

traffic.

Each ni node looks into the adjacency matrix at each tsand finds the connected component, ci

s, to which ni belongs

at ts. It then tries to find the first component whose mem-

bers have changed at least a fraction, 1 - k of them at ts,

where k is the average algebraic connectivity of cis for all

s = 1,…,w. Note that the algebraic connectivity is defined

to be the second-smallest eigenvalue of the symmetric

normalized Laplacian matrix of a component [16, 19]; the

symmetric normalized Laplacian matrix is defined as

follows:

Lnorm := I � D�12AD�1

2 ð1Þ

where I is the identity matrix, A is the adjacency matrix and

D is the degree matrix [5].

According to the Rayleigh–Ritz theorem [12], the

solution to the graph partitioning problem for two par-

titions is precisely given by the eigenvector correspond-

ing to the second smallest eigenvalue [26, 31, 34].

Unlike the traditional connectivity, the algebraic con-

nectivity depends not only on the number of nodes in the

graph but to what extent the nodes are connected to each

other. Thus, the algebraic connectivity captures the

membership change ratio of a component well, because a

component with a low algebraic connectivity may easily

be broken apart. Let ts be the time when at least a

fraction (1 - k) of the component’s members are chan-

ged for the first time. Then s - f is the period that at

least a fraction (1 - k) of the members are changed in

the component since tf, where f is initialized to 1. nikeeps finding the next such components and computes

the average period. In Algorithm 1, P denotes the set of

the (s - f) periods.

Table 1 Sample snapshot

information for node niTime Neighbor nodes

t1 n2, n3, n4

t2 n2, n5

t3 n4

… …tw n2, n7, n10, n12

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Algorithm 1 Determining change period

Period set: ;

for do

if then

end if

end forreturn the average of all the values in P

2. The compactness of components: In periodic pumping,

the diameter of the component at time ts is utilized as

the TTL of the forwarding message. Traffic congestion

may be reduced by the TTL, since a message can reach

the members in a component within the TTL. How-

ever, the diameter of the components may not be a

proper factor for determining the TTL. For instance, in

a graph, G = K100 [ P4; the diameter of G is five, but

the geodesic between most pairs of nodes is one. Thus,

if the TTL is set to five, unnecessary network traffic

would be generated. For this reason, we use the com-

pactness of a component, as in [3]. The compactness is

defined to be the sum of the inverse geodesic of con-

necting nodes with the normalization of n(n - 1),

where n is the number of nodes in a component. The

compactness of a component can be written as in the

following equation, where dij is the geodesic distance

between a pair of nodes, ni and nj, in the component.

compactness ¼P

i6¼j 1=dij� �

nðn� 1Þ ð2Þ

However, we cannot use the compactness directly for

the TTL, because the compactness is not related to the

diameter. We therefore devise an equation with the com-

pactness and the longest diameter, D(G), of all components

as follows.

T ¼ DðGÞ1�compactness ð3Þ

In Eq. (3), as compactness becomes 1.0, the TTL T is

close to 1.0, indicating that a short TTL is good for con-

nected components with high compactness. On the other

hand, as compactness becomes 0, T is close to D(G),

indicating that a long TTL is appropriate for connected

Fig. 1 Example of exchanging

snapshots

Wireless Netw (2015) 21:2055–2068 2059

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components with low compactness. Note that relationship

between TTL T and the compactness is non-linear, because

Eq. (3) is an exponential function. As the compactness is

increased from 0.0 to 1.0, T is rapidly decreased in the

earlier stage. However, as the compactness gradually

approaches 1.0, T decreases to 1.0 extremely slowly.

According to the percolation theory [32], before the com-

pactness reaches a critical point, the network topology

consists of many small-sized components, each of which

has a relatively large compactness. After reaching the

critical point, a giant component (a connected component

that contains a constant fraction of the total number of

nodes in a network) may suddenly emerge from the net-

work topology. Note that the compactness of the giant

component is very small, since the geodesics in the com-

ponent become much longer. Such relationship naturally

fits the non-linearity between the compactness and TTL.

3. The number of components with consideration to the

component size (the number of nodes): We want each

component to maintain at least one node, called the

messenger, which keeps the copy of the message and

which pumps the message as the sender node does.

However, if the number of messengers, k, is equal to

that of the components, there may be superfluous

network traffic, because some components may be

trivial in size and other non-trivial sized components

may get more than one messenger. To determine an

appropriate value for k, we incorporate the number of

components with the component size, as shown in Eq.

(4), where Cs is the number of components at time ts,

mis is the size of component i, i = 1,…,Cs at time ts, w

is the number of snapshots, and n is the number of the

nodes in the network.

k ¼P

s

Pi min ms

i � Csn; 1

� �

wð4Þ

In Eq. (4), msi � Cs

ndenotes the ratio of the size of compo-

nent i to the average size of the components. We call it the

density of component i. We set the maximum value of the

density to 1.0, since more than one messenger in a component

may generate unnecessary traffic. We obtain k by dividing the

sum of the densities of all components for all s by w.

Each node should determine k messengers in the network

that are more likely to meet the destination. To do so, each

node looks into each component to which the destination

belongs in all the snapshots and finds kmessengers that appear

the most in all the components belonging to the destination.

In Fig. 2, we assume that n1 is the sender, n10 is the

destination, and k = 3. To select the k messengers, n1 looks

into each snapshot and finds the component to which the

destination belongs. That is, {n6, n7, n8, n9, n10} at t1, {n9,

n10} at t2, {n4, n7, n10} at t3, and {n2, n4, n5, n9, n10} at t4.

Hence, n1 chooses the nodes that appear most in the

components; n9, n7, and n4 are selected as messengers

because n9 appears three times, and n7 and n4 appear twice

each.

In the forwarding phase, whenever n1 encounters n9, n7,

and n4 for the first time, let each messenger keep the copy

of the message. Note that the sender may not encounter all

of the messengers and hence there may be less than

k copies of the message during the forwarding phase. Each

messenger who received the message plays the same role

as the sender independently.

Step 3: As soon as the warm-up period ends, each node

determines the pumping period, TTL, and k messengers

from the extracted network features in Step 2. Each sender

then pumps the message with the IDs of the messengers to

its neighbors. Each neighbor node then sends them to its

neighbors, and so on. If the destination receives the mes-

sage, the delivery has been accomplished. Or, if a mes-

senger receives the pumped information, it then acts like

the sender. Such pumping lasts until the TTL is computed

by the messenger.

4 Performance evaluations

4.1 Simulation environment

Our simulation model is similar to that used in [11, 29]. We

used the network simulator, NS-2 v2.35 [18, 25], to eval-

uate our proposed scheme, Snapshot, because the NS-2 is

suitable for analyzing the correlation between the network

traffic and transmission delay.

We compared Snapshot with typical dissemination-

based schemes such as the epidemic, SimBet and PRo-

PHET schemes. In our simulation, 40 mobile nodes follow

the home-cell community-based mobility model (HCMM)

[2] which is a widely used mobility pattern in mobile

network simulations. The network area is set to

150 m 9 150 m with four special zones called home

communities. A home community can be defined as a set of

members who gather socially at a certain place. So the

members in the same home community spend more time

with each other at their physical place. Each home com-

munity has ten nodes of which only one is the traveler

node. A traveler node has more chances to encounter other

nodes of different communities so that it can generally acts

as a bridge between communities far apart, while a non-

traveler node mostly stays within its home community or

stochastically follows a traveler node. The speed of each

node is 2–10 m/s. A node can recognize other nodes within

1, 5, 10, 20, 30, 40, 50 m. Each node in the network ran-

domly selects a destination to send a message. We

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measured the delay time (s) and network traffic (the

number of received messages) until all 40 messages

arrived at their destinations. The simulations were con-

ducted 20 times to obtain the average results. The param-

eters for epidemic, PRoPHET and SimBet are given in

Table 2. Through extensive experiments the parameter

values have been determined in order for other schemes to

achieve their best experimental results in the environments,

while the proposed scheme is able to automatically adjust

its own parameters appropriately. Note that other schemes

should rely on manual adjustments of their parameters for

the environments. There is a warm-up period of 500 s.

During the warm-up period, each node gathers the snapshot

information in the form of an adjacency matrix. The pro-

posed scheme needs a warm-up period of 500 s. However,

its length is relatively short when compared with the ser-

vice time for the rest of the simulation that takes up to 12 h.

Such a lengthy period of time for the service time is not

unusual because DTN assumes very long end-to-end delays

due to lack of node contacts. In addition, the warm-up

period is only needed once in the beginning of network

services. Note that both SimBet and PRoPHET also require

the warm-up periods for collecting appropriate information

for their schemes like our proposed scheme and it is not

difficult to find other articles published that resort to the

warm-up periods [8, 9, 21, 23]. During the warm-up period,

each of PRoPHET, SimBet and Snapshot generates control

packets, while epidemic doesn’t need to generate any

control packets. Therefore, epidemic has more effective

than other schemes to reduce network traffic. In practice,

we have evaluated the number of received control packets

during the warm-up period of 500 s in the default network

environment. Snapshot, PRoPHET and SimBet exchange a

control packet whenever a node encounters another node;

Fig. 2 Snapshots at ts, where s = 1, 2, 3 and 4

Wireless Netw (2015) 21:2055–2068 2061

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each scheme uses about 26,000 control packets. However,

we assume that the size of a control packet is significantly

smaller than that of a data message packet because a

control packet in Snapshot has only a small size matrix of

binary information; that is, the size of a control packet is

500 times smaller than that of a data message packet. Thus,

the network traffic incurred by the control packets is neg-

ligible in analyzing the performance of Snapshot. Table 2

summarizes the parameters of the simulation environment.

In Fig. 3, the shaded cells indicate the locations of the four

communities.

4.2 Simulation results

Figure 4 presents the average network traffic and trans-

mission delays of epidemic, SimBet, PRoPHET, and

Snapshot. In the Fig. 4, the network traffics of epidemic,

SimBet, and PRoPHET are about 454.3, 323.6 and

223.9 % larger than that of Snapshot, respectively. The

transmission delay time of Snapshot is about 23.6 and

6.0 % smaller than those of SimBet and PRoPHET,

respectively. As we expected, Snapshot significantly

reduces the network traffic while maintaining a reasonable

delay time, because Snapshot maintains proper control

values, as given in Table 3.

We tested Snapshot for the above three control values in

dense networks to verify why Snapshot could reduce net-

work traffic significantly with a comparable delay time.

Snapshot was first tested with ten different pumping peri-

ods (1–10 s), as shown in Fig. 5, to verify that a proper

value for the pumping period is three. The Fig. 5 shows

that when the pumping period is three, Snapshot performs

quite well in terms of both network traffic and delay; when

it is two, traffic increases but the delay remains similar. On

the other hand, when it is four, not much changes with the

traffic but the delay gets longer. For other pumping periods,

there are wider gaps in the results. This is especially the

case when the pumping period is equal to or longer than

four; there are more nodes that do not get the messages,

resulting in a longer delay time with a smaller amount of

network traffic.

Next, we tested Snapshot with ten different numbers of

messengers, as shown in Fig. 6, to verify that the proper

number of messengers is three. Note that we obtained the

number of components for the number of messengers. In

Fig. 6, when there are three messengers, Snapshot per-

forms best in terms of both network traffic and delay time.

When there are four or more messengers, the network

traffic increases and the delay time improves slightly,

because more nodes receive duplicate messages from the

messengers. Hence, Fig. 6 confirms that three is indeed

properly chosen as the number of components.

Finally, we show that the average TTL chosen by

Snapshot successfully reduces the network traffic. After

the warm-up period, Snapshot determines the average

TTL to be nine with DðGÞ1�compactnessof the components

in each snapshot. Note that the average TTL is the longest

diameter among all of the components. We tested Snap-

shot with ten different TTLs (3–12). Figure 7 shows that

when the TTL is nine, Snapshot exhibits the least amount

of network traffic with almost the shortest delay time.

When the TTL is less than nine, the performance is poor,

because a message may not be spread into all the nodes in

a component.

4.3 Results with various communication ranges

We measured the network traffic with various communi-

cation ranges between 1, 5, 10, 20, 30, 40, 50 m. Figure 8

shows the simulation results of epidemic, SimBet, PRo-

PHET, and Snapshot. Both epidemic and SimBet increaseFig. 3 Community pattern

Table 2 Simulation parameters

Parameter (unit) Value (default)

Number of nodes 40

Size of the network (m2) 150 9 150

Number of communities 4

Community size (m) 50 9 50

Node speed (m/s) 2–10

Radius of communication range (m) 1, 5, 10, 20, 30, 40, 50 (30)

TTL for epidemic, PRoPHET, SimBet 10

Control value a for SimBet 0.5

Transitivity factor for PRoPHET 0.2

Aging factor for PRoPHET 0.8

Initial probability factor for PRoPHET 0.2

Number w of snapshots taken 50

Warm-up period (s) 500

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network traffic as the communication range gets longer,

since more nodes could communicate with each other

directly. PRoPHET shows a similar trend as epidemic, but

when the communication range is 10 m, PRoPHET gen-

erates more network traffic than epidemic because PRo-

PHET requires a longer time to send all 40 messages to the

destinations. Note that we measured the delay time and

network overhead until all 40 messages arrived at their

destinations. On the other hand, Snapshot maintains low

network traffic with various communication ranges because

our scheme controls the number of messengers, the length

of the pumping period and the TTL according to the net-

work environment.

We also investigate the transmission delay with various

communication ranges. Figure 8 shows that epidemic

exhibits the shortest delay in each communication range.

The transmission delays of all the schemes are reduced as

the communication range increases. When the range is

50 m, Snapshot exhibits an almost similar delay time to

epidemic, since our scheme deploys an appropriate number

of messengers.

DTN routing schemes should allow reasonable trans-

mission delay and network traffic because DTN basically

assumes very sparse network environment. Thus, we also

measured the transmission delays and network traffics with

Fig. 4 Average network traffic and transmission delay in the default network

Fig. 5 Average network traffic and transmission delay with various pumping periods

Table 3 The average control values of snapshot

Snapshot controller Value

Pumping period 3

The number of messengers 3

TTL T 9

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Fig. 6 Average network traffic and transmission delay with various numbers of messengers

Fig. 7 Average network traffic and transmission delay with various static TTLs

Fig. 8 Performance results with various communication ranges

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the communication ranges of 1 and 5 m. In such very

sparse environments, the schemes show very similar trends

to those in other progressively dense environments. SimBet

shows very poor performance in very sparse networks

because it is extremely difficult for a node to find its

neighbors. If nodes hardly find the neighbor nodes in

SimBet, the similarities and betweenness utility values of

nodes have unintended meanings. However, as shown in

Fig. 8, Snapshot has well adapted to the sparse environ-

ments, because Snapshot seems to mimics epidemics by

adjusting the compactness, TTL, and period values

appropriately

4.4 Results with limited memory space

Figure 9 compares the robustness of the schemes in terms

of the memory space. The unit of memory space is the

number of slots, where each message fits into a single

slot. The results clearly indicate that the memory size of

our proposed scheme barely affects the transmission delay

time and the network traffic because the proposed scheme

uses the pumping method. Note that the pumping method

allows relay nodes to pass messages without keeping

them in their memory. However, the carry and forward

schemes such as epidemic, SimBet and PRoPHET permit

each relay node to keep the messages in its memory.

Therefore, these schemes may be easily influenced by

memory size.

According to Fig. 9, the larger the memory size is of the

schemes, the less network traffic that is acquired. Note that

a longer transmission delay usually incurs more network

traffic, because we stop the experiment when all 40 mes-

sages are successfully delivered. As expected, a larger

memory size leads to a reduction in the transmission delay

(Fig. 9).

4.5 Results with various community patterns

We measured the network traffic and transmission delay

with various community patterns in order to show the

robustness of the proposed scheme. We have chosen a few

other community patterns as shown in Fig. 10. They are

chosen according to the dispersion of the communities

within the network area; that is, we want to have a few

typical patterns depending on how communities are close

to each other. Note that the distance between a pair of

communities decides the distances that the nodes belonging

to the communities move around. The default community

pattern in Fig. 3 represents the most dispersed pattern,

while Fig. 10c represents a more concentrated pattern and

Fig. 10a, b represent intermediate patterns when compared

with both Figs. 3 and 10c.

In Figs. 11, 12 and 13, the simulation results in the

community patterns show very similar trends each other.

For epidemic, the average network traffic of the three

patterns in Figs. 11, 12 and 13 (the sum of traffics in the

three figures/3) is 15.0 % smaller than the network traffic

in Fig. 4. Such traffic reductions are attributed to the fact

that the messages are delivered earlier in the three com-

munity pattern environments of Fig. 10 than in the default

pattern environment. Note that we measured the delay time

and network overhead until all 40 messages arrived at their

destinations.

For SimBet, PRoPHET, and Snapshot, the average

traffics in Figs. 11, 12 and 13 are 15.6, 27.4, and 35.0 %

larger than the traffics for the default case in Fig. 4,

respectively. However, for epidemic, SimBet, PRoPHET,

and Snapshot, the average delay results in Figs. 11, 12 and

13 are about 3.5, 6.6, 12.8, 23.6 % smaller than the delays

for the default case in Fig. 4, respectively. Larger traffics

and shorter delays of the schemes are caused by the fact

Fig. 9 Performance results with various memory spaces

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that in HCMM a node mostly moves from its community to

another community, and hence shorter inter-community

distances in the three community pattern environments of

Fig. 10 contribute to shorter traveling distances of nodes as

well as more frequent encounters among the nodes.

5 Conclusions

Our work examined two main questions, the first of which

is how to devise a new carry and forward scheme that is not

sensitive to the size of memory space. We provide the

(a) The first pattern (b) The second pattern (c) The third pattern

Fig. 10 Various community

patterns

Fig. 11 Average network traffic and transmission delay for the pattern in Fig. 10a

Fig. 12 Average network traffic and transmission delay in the pattern in Fig. 10b

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pumping method in response to this question. The pumped

messages are forwarded to the neighbors right after they

are received without keeping them in the memory space. In

addition, pumping is periodically performed in each node.

By applying this pumping process, we devise a forwarding

scheme which is not sensitive to memory size. Therefore,

by reducing the reliance on memory size, the proposed

approach performs well at forwarding a message in an

environment that has limited memory or deals with large-

sized messages. However, this pumping approach itself

generates high network traffic and creates a longer trans-

mission delay. Therefore, we employed a graph theoretical

notion called the compactness of each component in order

to control the TTL.

The second main question we have addressed is how to

analyze a network topology in opportunistic networks and

how to exploit the features of a network topology. We

provided a snapshot mechanism so as to get a network

topology in a distributive manner. In the Snapshot scheme,

each node stores the social interactions for a certain period

of time. Each node then exchanges the stored social

interactions. The interactions are accumulated in the form

of an adjacency matrix to represent a network graph at a

specific time. We extracted two other essential features of a

network topology, the change period of membership in the

component and the number of components with consider-

ation to the component size.

The extensive simulation results show that the utiliza-

tion of the three network topology features is quite effec-

tive, and also our scheme outperforms other approaches in

terms of the transmission delay and network traffic. We are

currently working on the impact of different network fea-

tures with social network concepts.

Acknowledgments This research was supported by the Basic Sci-

ence Research Program through the National Research Foundation of

Korea (NRF) funded by the Ministry of Education, Science and

Technology (2013R1A1A2011114).

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Junyeop Lee is currently an

M.S. candidate in Computer

Science at Yonsei University in

Korea. His research interests

include mobile social networks,

delay tolerant networks and

social network analysis.

Sun-Kyum Kim received his

M.S. in Computer Science from

Yonsei University in Korea in

2012. He is currently a Ph.D.

candidate at Yonsei University.

His research interests include

mobile social networks, delay

tolerant networks and social

network analysis.

Ji-Hyeun Yoon is currently an

Ph.D. candidate in Computer

Science at Yonsei University in

Korea. His research interests

include mobile social networks,

delay tolerant networks and

social network analysis.

Sung-Bong Yang received his

M.S. and Ph.D. from the

Department of Computer Sci-

ence at the University of Okla-

homa in 1986 and 1992,

respectively. He has been a

professor at Yonsei University

since 1994. His research inter-

ests include graph algorithms,

mobile computing, and social

network analysis.

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