[acm press the 8th acm international workshop - bodrum, turkey (2010.10.17-2010.10.18)] proceedings...

On Quantifying the Quality of CDS-based VirtualBackbones in Mobile Ad hoc Networks

Julien SchleichUniversity of Luxembourg

FSTC - CSCLuxembourg

[email protected]

Grégoire DanoyUniversity of Luxembourg

FSTC - CSCLuxembourg

[email protected] Bouvry

University of LuxembourgFSTC - CSCLuxembourg

[email protected]

Le Thi Hoai AnUniversity Paul Verlaine - Metz

LITAFrance

[email protected]

ABSTRACTWe propose to study the quality of CDS-based virtual back-bones generated by fully distributed algorithms in mobileenvironments. As virtual-backbones may be used for differ-ent purposes, the importance of a characteristic may varyaccordingly. In order to deal with this variety issue, weprovide a set of quality criteria quantifying different suit-able aspects for virtual backbones in mobile ad hoc net-works. Distributed and localized algorithms are then com-pared through simulations with respect to these measuresand criterion-specific optimizations are proposed for the Black-bone2 algorithm.

Categories and Subject DescriptorsC.2.1 [Network Architecture and Design]: Network topol-ogy, Wireless communication; G.2.2 [Graph Theory]: Net-work problems, Graph algorithms

General TermsAlgorithms, Design, Performance, Theory

Keywordsk-connected m-dominating Set, Wireless Ad hoc Networks,Localized algorithm

1. INTRODUCTIONAd hoc networks distinguished themselves clearly from

other communication networks with many features such asabsence of a fixed infrastructure, wireless multi-hop commu-nication, and strict resource limitations (e.g., limited band-width and energy). Mobile ad hoc networks additionally

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.MobiWac’10, October 17–18, 2010, Bodrum, Turkey.Copyright 2010 ACM 978-1-4503-0277-7/10/10 ...$10.00.

consider mobility of the network nodes, which induces changesin the network topology through time. Protocols build ontop of these networks should be resilient to these mobilityaspects (not up-to-date paths, partitioned network) and stillremain efficient considering the scarce available resources.

In wireless ad hoc networks, the shared medium and thelack of global coordinator imply that the node throughputdeclines rapidly to zero as the number of nodes in the net-work increases [8]. In order to deal with large-sized net-works, the creation of a virtual backbone is a commonlyproposed solution [5, 9, 16–18]. Backbone formation lever-ages the scalability limits of traditional routing for ad hocnetworks by selecting a subset of the network nodes, the so-called backbone, that is responsible for performing and man-aging multipoint communication (routing, multicast, broad-cast).

One of the most studied solution to create a virtual back-bone is the computation of a Connected Dominating Set(CDS) in the communication graph representing the network[5, 9, 16–18]. Given a simple undirected graph G = (V, E),where V is a set of vertices representing the hosts and E isa set of undirected edges representing the links. A subsetV ′ ⊂ V is a dominating set of a graph G = (V, E) if everyvertex not in V ′ is connected to at least one member of V ′

by some edge. A subset V ′′ ⊂ V is a connected dominat-ing set of graph G = (V, E) if V ′′ is a dominating set ofG and the subgraph induced by V ′′ is connected. As ex-plained in [7] the usefulness of CDS has been demonstratedin protocols that perform a wide range of communicationfunctions such as media access coordination, unicast, multi-cast/broadcast, location-based routing, energy conservationand topology control.

In the literature, it is well-established that the qualityof a CDS depends on its size corresponding to the numberof nodes in V ′′. Indeed, if less nodes are in charge of therouting process, the overhead due to routing will be lessimportant. The problem of finding the CDS of the smallestsize is called Minimum CDS and many approximation orheuristic algorithms have been proposed [2,5,17,18] to solvethis problem in a distributed way with local information.

The major drawback of the CDS approach in a mobilead hoc context is its poor reliability due to node failure.Indeed, loosing one node that is part of the virtual back-

21

bone may induce its breakage. To increase the robustnessof the backbone, a more general problem has been studied:the minimum k-connected m-dominating set problem. Theobjective here is to increase the connectivity of the virtualbackbone to the value k (k ∈ N+) and the minimal domi-nation value to m (m ∈ N+). Increasing the connectivitycreates backup routes inside the virtual backbone and in-creasing the domination creates backup access points to thevirtual backbone. In this paper we propose new variantsof Blackbone2, a fully decentralized algorithm using localknowledge for creating km-CDS backbones.

Whatever the proposed solutions, their performances arealways compared thanks to a simple and straighforward mea-sure: the size. The less backbone nodes there are, the betterit is. This is true in static networks in which the robust-ness of the solution is not a major criterion. However, thismay not be adapted in mobile networks, because of frequenttopology changes, not up-to-date or incomplete information.In our work, we propose additional virtual backbone qualitymeasures to quantity the suitability of a backbone throughtime. Moreover, we test the performances of our previousalgorithms [12, 13] in mobile context with respect to thesemeasures.

The remainder of this paper is organized as follows. InSection 2, we review some existing CDS and k, m-CDS con-struction algorithms. In Section 3, we present the prob-lem of quantifying good solution in a mobile context andwe propose some measures. Section 4 briefly presents themain algorithm and some heuristic optimizations for deal-ing with volatile topologies and in Section 5 we evaluate theperformances of the different algorithms through simulation.Finally, we conclude this paper and discuss some future re-search directions in the last section.

2. RELATED WORKDesigning k, m−CDS based virtual backbone algorithms

has been a prolific topic of research during the last ten years.However the major part of these works deals with staticnetworks only. In a first part we provide a literature surveyfor a first class of solutions called centralized approximationalgorithms. Then we summarize some major contributionsfor the distributed algorithms. Finally we review what hasbeen done to deal with the mobility issues.

2.1 Centralized approximation algorithmsMost of the centralized contribution are approximation

algorithms. These algorithms are compared using their ap-proximation function f(n), with n the number of nodes inthe network and f(n), a mathematical function. Such ap-proximation factor means that in the worst case, the sizeof the solution produced by the algorithm is f(n) times thesize of the optimal solution. To obtain these guaranteedproperties, the authors generally restrained their analysesin a specific class of graphs: Unit Disk Graphs (UDG [4]).In [14, 15, 19], the authors proposed centralized algorithmsto solve some instances of the general k, m-CDS problem. In[15], Wang et al. proposed CDSA, a 64-approximation cen-tralized algorithm that is only applicable in the case wherek = 2 and m = 1. Shang et al. [14] proposed three cen-tralized algorithms to construct 1-connected m-dominatingset, 2-connected m-dominating set, and k ≥ 3-connected m-dominating set. Wu et al. [19] proposed CGA, a centralizedalgorithm which firstly creates a m-dominating set and then

augments it until it becomes k-connected. In [20], the au-thors proposed a centralized algorithm, ICGA, characterizedby a constant performance ratio for general values of k andm.

2.2 Distributed algorithmsCentralized algorithms are generally obtaining better the-

oretical and simulation results, as they benefit from the com-plete knowledge of the network. However gathering suchknowledge in one or all the node is not realistic in mobilead hoc networks for two main reasons. First, gathering thecomplete topology induce a lot of message exchanges andthus reduces the available bandwidth for real communica-tion. Second, as nodes may move through time, it is veryunlikely to gather an up-to-date topology at a given time t.

For the case k = m = 1 many different algorithms can befound in the literature [2, 5, 10, 18]. Wu et al. [18] proposeda localized connected dominating set approach, based on anode marking rule (true means in the backbone) and twopruning rules. A generalization of the pruning rules hasbeen proposed by Dai et al. [5]. This rule checks if a set of knodes covers the neighbor set. In [3], the authors proposeda simulation-based comparison of the most representativesolutions to create CDS. They considered various criteria tocompare the algorithms: the overhead of the algorithm, theenergy consumption per node, the backbone size, the routelength in the backbone and a robustness criterion. Thisstudy provides very detailed insights concerning the testedalgorithms but only consider static networks.

Decentralized algorithms have also been proposed to solvesome instances of the general k, m-CDS problem in [6,19,20].Dai et al. proposed three localized k = m-CDS algorithms,where k = m. The first one is a probabilistic approach whichrequires the network size and the node density to compute aprobability pk of a node k to be in the backbone. The secondone maintains a fixed node degree in the backbone and alsorequires network size and density. The third one is a deter-ministic approach which is an extension from the coveragecondition introduced by the same authors to construct 1, 1-CDS [6]. This approach checks if there are k independentpaths composed of high priority nodes between each pair ofneighbors. In [19], the authors proposed a distributed ver-sion of CGA called DDA. However, DDA requires a hugenumber of messages, which is a major drawback for a realapplication in ad hoc networks. In [20], a distributed algo-rithm, LDA, is proposed to overcome the problems of DDA.However, it requires the maximal node degree to be constantand it uses CDS-BD-D [9], which implies the election of aroot node in the network.

2.3 MobilityAs previously mentioned, very few works have tackled the

effects of mobile environment which brings new challenges interms of algorithms robustness and performance metrics. In-deed the vast majority of the literature only considers staticnetworks. As an exception, some interesting conclusions canbe found in [1] in which two different approaches to constructCDS are compared with respect to some communication pro-tocol metrics such as collision rate, coverage percentage ofbroadcast packets or bandwidth usage. These types of met-rics are very important when real implementation is con-sidered, however results are only sound with the selectedcommunication protocols and may vary a lot with different

22

configurations. Interesting work about metrics in dynamicgraphs can also be found in [11]. These propositions aregood indicators of the dynamicity of a graph but are notdesigned for quantifying the quality of a virtual backbones.

3. QUALITY IN MOBILE ENVIRONMENTSIn the first part of this section, we explain why it is much

more complicated to quantify the quality of a CDS in amobile context. In the second part, we detail the differentimportant criteria related to quality in a mobile environmentand we propose some quality measures.

3.1 Mobile environmentIn a static context, the communication graph is barely

changing through time. Some nodes may appear or disap-pear, depending on the type of events included in the sim-ulation, but generally the graph is not changing at all. Forthese types of network, measuring the quality of a CDS isstraightforward: it has to be as small as possible, i.e., thecardinality of the connected dominating set should be min-imal.

In mobile environments, the size of the connected dom-inating set is still an important criterion as more compactbackbones induces less protocol overhead (better energy ef-ficiency and better bandwidth usage). However, reducingthe number of nodes in the virtual backbone may not helpfor two reasons.

First, the CDS construction algorithm has to adapt itselfto the changing topology. As a matter of fact, having a verycompact CDS may require more maintenance. A direct con-sequence of this conclusion is the fact that the virtual back-bone is not stable through time. Let us not forget that thesebackbones are intended to be used by higher-layer protocolsfor which stability is an important criterion (e.g. routing orbroadcast protocols).

Second, nodes require information to take local decisions.These pieces of information are generally gathered with bea-con packets or specific control messages. However, due totopology changes or radio related problems, the local infor-mation of some nodes may be inconsistent (e.g. some neigh-bors may not be reachable anymore) or incomplete. As localdecision are based on these pieces of information, wrong de-cisions may be taken by some nodes, and the set of selectednodes may not be a CDS during some time, i.e. some nodesmay not be covered. As a consequence, we think that a ro-bust virtual backbone algorithm should be able to withstandthese kind of adverse situations and that its ability shouldbe quantified using specific quality metrics.

3.2 Quality measuresIn this work, we propose to select a small set of qual-

ity measures for quantifying different suitable aspects for aCDS-based backbone in a mobile context. We first definethree notions relative to the quality of a backbone throughtime: size, stability, and availability. These three charac-teristics may have different importances depending on whatscenario or protocol is considered. However, aggregatingthese measures with different weight values to compare theperformances of some algorithms is not in the scope of thiswork. We will focus on giving fair results for all the differentmetrics in order to have a clear idea of the algorithms rawperformances.

For the remaining of this work, let V B(Gm) be the virtualbackbone built on top of the graph Gm. Let consider thatthe simulation time t is discretized and composed of T steps,ti ∈ {t1, . . . , tT }.3.2.1 Size

As previously mentioned, the size of the CDS has a majorimpact on the quantity of maintenance or protocol messagesand thus on the available bandwidth for real communica-tion. In a static context, we just have to count the numberof nodes in the backbone. However, how to apply this no-tion to a dynamic communication graph? A straightforwardidea would be to save a series of size measures on a fixedfrequency and to compute the average value. However thismay not detect an algorithm that offers really compact andnear optimal structures at some time of the simulation andvery large ones at some other. Therefore we propose to use amore complete statistical data set (e.g. mean, median, min,max, standard deviation) to have a more detailed view ofyour algorithm behavior concerning the backbone size (seeMeasure 1). To obtain a network-size independent set ofmeasures, consider percentage of backbone nodes instead ofthe size of the backbone.

Measure 1. Mean, median, minimal, maximal and stan-dard deviation of the series of values {V Bt(Gm)}t∈{t1,...,tT }.

3.2.2 StabilityThe stability of the backbone is generally an antagonist

notion of the size. It is indeed straightforward that hav-ing the smallest possible backbone requires frequent main-tenance to adapt quickly to the topology changes. Somemay however argue that it also depends on how well nodesare chosen.

A stable backbone is suitable for higher-level services suchas broadcast or routing, because it reduces their needs ofcontrol messages. Indeed, in a stable backbone, updatingthe routing paths can be done less often. A simple idea tocompare algorithms requirements is to count the number ofnodes going in and out of the backbone during the simulationtime. The details are presented in measure 2. For a networksize independent measure, we can average the number ofchanges by the number of nodes.

This measure is really simple but it does not quantify thestability of the backbone versus the stability of the network,i.e. the values of this measure highly depends on the sim-ulated scenario. This type of measurements is well-knownin the ad hoc clustering domain in which finding the moresuitable nodes as representatives (cluster-heads) is a majorobjective.

This work does not take into account the protocols basedon top of the backbone. However, it can be envisaged to cre-ate a protocol-specific measure that would count the over-head induced by the backbone (size and stability) comparedto an optimal solution.

Measure 2. Let Cti the set of nodes that change theirstates at time ti. Counting the number of changes during thesimulation is achieved via statechange =

P{ti}t1,...,tT

|Cti |

3.2.3 AvailabilityMobility creates inconsistencies between local information

gathered by all nodes and the communication graph. Asa consequence, wrong concurrent and distributed decisionsmay lead to:

23

• not exactly one backbone per connected component

• isolated nodes, i.e. non-dominated non-backbone nodes

In both cases, some couples of nodes may not be able tocommunicate using the virtual backbone despite an existingroute in the communication graph. In order to quantifythese problems we propose two straightforward measures, 3and 4. Measure 3 keeps track of the number of connectedcomponent in the communication graph and in the the graphinduced by the virtual backbones. The computed ratio canhave different values ranges which represents different cases:

• ratio = 1, the generated backbones are likely to fit theconnected components of the communication graph.

• ratio < 1, as more backbones than connected com-ponents exist, some nodes inside the same connectedcomponent may not be able to communication via thebackbone.

• ratio > 1, this case may happens if the backbone isnot adapting quickly enough to the topology changes.

Measure 4 keeps track of the number of isolated nodes, i.e.non-backbone nodes with no backbone node in its directneighborhood.

Measure 3. Ratio between the number of connected com-ponent, |CC|, of the graph Gm and the number of con-nected components of the backbone nodes induced subgraph,|CCV B |.

Measure 4. Number of isolated nodes, i.e. non-backbonenode not covered by any backbone node.

4. OPTIMIZING BLACKBONE2In a first time we briefly present the Blackbone2 charac-

teristics [13]. Various optimizations are then proposed toobtain better performances in mobile environments.

4.1 Blackbone2 CharacteristicsAll the proposed k, m−CDS algorithms of the literature

have a defined number of steps to create their solution.These algorithms have a proven convergence property buttheir exploration of the solution space is monotonous: nodesare added (resp. removed) from the solution until all stepsare processed. Moreover, these algorithms generally requirean implicit synchronization: all nodes have to process step nbefore starting step n+1. This requirement directly impliesthat these algorithms are not self-healing: without synchro-nization, inconsistencies may happen.

In our case, even if all our simulations converged, we can-not prove convergence for the genuine version of the algo-rithm. Nodes may get in and out of the backbone indefi-nitely and never find a steady state. However this bad prop-erty has a major advantage: the algorithm is not stuck inthe feasible solution space, i.e. at some moment the so-lution may be inconsistent. This induces that the algo-rithm can reach solutions that are impossible to achieve withmonotonous behavior.

Blackbone2 is an efficient algorithm using two colors topartition a given graph. If a node v is black (resp. white,it means that v is part (resp. not part) of the virtual back-bone. The color of a node at a given time depends on itscurrent state and its local knowledge: the subgraph Gv, rep-resenting what v knows about its neighbors. The Blackbone

2 algorithm is based on two simple symmetric rules. Theserules check two important characteristics: the first one isthe domination value and the second one is the connectiv-ity. Depending on these two checking results and its currentcolor, a node takes the decision to change or keep its currentcolor for a next round. More details can be found in [13].

4.2 OptimizationsIn a first time we propose techniques to reduce the subset

of neighbors considered to take local decisions. The secondtype of optimization aims at increasing the stability by fixingthe state of some interesting nodes.

4.2.1 Reducing the considered subgraphThis second optimization type is designed to increase the

stability measures. The main idea is that it may not be effi-cient in terms of maintenance if the nodes adapt themselvesto any topology changes. In fact, nodes should only con-sider useful nodes in their checking thus extra state changeswould be avoided.

We propose two straightforward and yet different heuris-tics to filter useless nodes:

• the age of a node (age threshold variant), i.e. we con-sider as neighbors nodes we know for enough time

• the relative speed of a node (relative speed thresholdvariant), i.e. we consider as neighbors nodes with aslow enough relative speed

The main difference between these two heuristic choices isthat relative speed may be more precise due to extra infor-mation. Indeed, the Blackbone 2 algorithm is working withspecific beacon packets containing list of neighbors and theiruseful details. For a given node, computing the age of itsneighbors can be done by counting the number of beaconreceived from them. However no geographical data is pro-vided by the beacons. To overcome this problem we proposetwo solutions:

• the nodes are equipped with a GPS chip or any loca-tion based device and positions are added to the bea-con packets.

• the nodes may estimate the distance to their neighborsthanks to the signal strength evaluated while receivingbeacon packets.

The first solution may be more precise to estimate absolutedistances because it relies on two dimensional data and notevaluation of a distance. However, the precision of the GPSmethod is based on the assumption that we are in a obstacle-free simulation space. This problem is overcome with thesignal strength as this measure is representing the quality ofthe communication link. The second solution is a cross-layeroptimization as it requires access to lower-level data.

4.2.2 Fixing the state of some nodesThe major problem of the Blackbone2 algorithm comes

from the unbounded number of computation steps until con-vergence, i.e. the nodes may be changing states for sometime until they are fixed. This is due a sort of domino ef-fect: a node that changes its state may create a chain ofreactions. In order to reduce these changes of state we pro-pose two heuristic choices:

• If a node is in the backbone and it has the highest num-ber of neighbors amongst its neighbors then it stays inthe backbone (high degree variant).

24

• If a node is in the backbone, it waits a given amountof time before considering the possibility of leaving it(forced stability variant).

The first heuristic choice gives more importance to higherdegree nodes because more nodes may rely on them. Thesecond heuristic reduces the blinking problem, i.e. nodes inthe same part of the network that keep changing state. Thisproblem is mainly due to the asynchronous nature of oursimulations: a node v may take a different solution if it hadreceived a packet from its neighbor w that just changed itsstate.

5. NUMERICAL RESULTSThe first subsection provides a description of the major

parameters used for our simulations. A subsection is dedi-cated to explaining why age and speed threshold are not suit-able to increase the stability. Finally the last two subsectionspresent a comparison based on the three quality character-istics of Blackbone2 and its new variants to the well-knownalgorithm by Dai et al. in [5]. A comparison summary high-lights the most important conclusions and closes the section.

5.1 ParameterizationThe simulator used for all the experimentation is OMNeT+

+ version 3.3p1 with the Mobility Framework version 2.0p3.The first series of tests were used to fine tune the algorithmparameters:

• The beaconing period, TB = 500ms

• The checking period that updates the state of a node,TCh = 500ms

• The periods related to mobility: when to remove anode from the 1 or 2-hop neighborhood, TRm1 andTRm2. Both periods are set to 2000ms.

During the initialization of the simulation, the nodes starttheir beaconing process at a time defined by a random num-ber. The randomness reduces collisions at the beginning ofthe simulation. The simulation space is a 215x125 metersrectangle. The transmission range has been fixed to 25 me-ters. These experiments have been repeated for differentnumbers of nodes (20, 30 up to 100) which permit to obtaina wide range of average node degree or density [0, 10].

We want to test the algorithms in high mobility condi-tions, we chose to use the random mobility model. We areaware that this model does not mimic any realistic behav-ior. However, we think that this artificial mobility modelmay represent the worst case in terms of stability for thecommunication graph because of its randomness and thus itis a particularly challenging benchmark. In a particular sim-ulation sim, all nodes of the network have the same speedssim ∈ [0 : 7] meters per seconds.

For each network size and for each speed value we run30 different simulations in order to compute average values.The run number is also used as a seed for the random numbergenerator used by OMNeT ++ to assign the initial positionof the nodes and produce their movements.

The different versions of the algorithm have also beentested with different parameter values. The heuristics thatreduces the considered subset of nodes by selecting nodesold enough has been tested for different age threshold valuesequal to Tha = x ∗ThB with x ∈ [0 : 10]. The case Tha = 0correspond to the regular algorithm. The second reduced

5

10

15

20

25

30

35

40

45

20 30 40 50 60 70 80 90 100

Nodes

in t

he

bac

kbone

(in p

erc)

Nodes in the network

Dai and WuBlackbone 2

Forced stability variantHigh degree variant

Figure 1: Influence of the density on the backbonesize (k = m = 1)

0

10

20

30

40

50

60

70

20 30 40 50 60 70 80 90 100N

odes

in t

he

bac

kbone

(in p

erc)




Figure 2: Influence of the density on the backbonesize (k = m = 2)

23

24

25

26

27

28

29

30

31

32

0 1 2 3 4 5 6 7

Nodes

in t

he

bac

kbone

(in p

erc)

Speed of the nodes (in m/s)



Figure 3: Influence of the speed on the backbonesize(k = m = 1)

34

36

38

40

42

44

46

48

50

0 1 2 3 4 5 6 7

Nodes

in t

he

bac

kbone

(in p

erc)




Figure 4: Influence of the speed on the backbonesize (k = m = 2)

25

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

20 30 40 50 60 70 80 90 100

Aver

age

num

ber

of

stat

e ch

anges

per

node

per

sec

ond




Figure 5: Influence of the density on the number ofstate changes (k = m = 1)

0

0.05

0.1

0.15

0.2

0.25

0.3

20 30 40 50 60 70 80 90 100

Aver

age

num

ber

of

stat

e ch

anges

per

node

per

sec

ond




Figure 6: Influence of the density on the number ofstate changes (k = m = 2)

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7

Aver

age

num

ber

of

stat

e ch

anges

per

node

per

sec

ond




Figure 7: Influence of the speed on the number ofstate changes (k = m = 1)

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7

Aver

age

num

ber

of

stat

e ch

anges

per

node

per

sec

ond




Figure 8: Influence of the speed on the number ofstate changes (k = m = 2)

0

0.5

1

1.5

2

2.5

20 30 40 50 60 70 80 90 100

Aver

age

num

ber

of

isola

ted n

ode




Figure 9: Influence of the density on the averagenumber of isolated nodes (k = m = 1)

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7A

ver

age

num

ber

of

isola

ted n

ode




Figure 10: Influence of the speed on the averagenumber of isolated nodes (k = m = 1)

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

20 30 40 50 60 70 80 90 100

Aver

age

rati

o d

uri

ng s

imula

tion




Figure 11: Influence of the density on the connectedcomponents ratio (k = m = 1)

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 1 2 3 4 5 6 7

Aver

age

rati

o d

uri

ng s

imula

tion




Figure 12: Influence of the speed on the connectedcomponents ratio (k = m = 1)

26

subgraph optimization considers nodes with a small enoughrelative speed. Different speed threshold, Ths ∈ [0 : 10]have also been tested. The regular algorithm corresponds toTh =∞. The last optimization that requires an additionalparameter is the forced stability version. The period forwhich a backbone node has to stay before considering leav-ing it is also based on the beacon period: Thstab = x ∗ ThB

with x ∈ [0 : 7].

5.2 Age and speed threshold do not workThe idea behind the usage of threshold concerning the age

of the relative speed between nodes is quite straightforward.Indeed, nodes should preferably consider stable neighbors asthey are more likely to help achieving successful communi-cation sessions. Having a higher threshold was not supposedto reduce the backbone size but it was expected to increasethe stability as the backbone should have been less sensitiveto short term topology changes, i.e. new neighbors quicklydisappearing.

However, it seems that having such threshold is not help-ing, at least with the random mobility model. We obtainedpoor results for both age and speed threshold which are mostprobably induced by the randomness nature of the chosenmobility model. However, we think that using this modelis important as it can be considered as the worst possiblescenario.

5.3 Performance comparison for each qualitycriterion

In this subsection we compare the performances of the dif-ferent Blackbone 2 variants and the Dai and Wu algorithmwith respect to the previously presented quality measures.We have chosen this algorithm as it is the only one fitting ourrequirements. First, the algorithm should be distributed andit should rely on local information only. Second, it shouldbe composed of one computational step as multiple-step al-gorithms rely on synchronicity which is not suitable in anasynchronous environment.

5.3.1 SizeIn Fig. 1 and 2 we can observe the percentage of nodes

used by the different algorithms versus the increasing sizeof the network. The genuine version of the algorithm andthe high degree variant show the most compact backbonesindependently of the required robustness: k = m = {1, 2}.The forced stability variant gives also very encouraging re-sults when the robustness is set to 2. Dai and Wu obtainbetter performances than the forced stability variant in oneparticular case: low robustness (k = m = 1) and densenetworks.

In Fig. 3 and 4 the backbone size performance is displayedversus the speed of the nodes. We observe the same kindof results than previously: best results are achieved by thegenuine algorithm and the high degree variant. An addi-tional interesting information is that these two algorithmsare characterized by their steadiness: the size of the solu-tions remain stable. In the low robustness backbones, theDai and Wu algorithm achieves better results when the mo-bility is higher. The forced stability variant however, showan inclination to build less compact solution when the nodesmove quickly. This problem is almost overcome when deal-ing with more robust backbones.

5.3.2 StabilityIn Fig. 5 and 6 we can observe that the algorithm creating

the most stable backbone is Dai and Wu. This big differenceis due to one main reason: in the Dai and Wu algorithm, anode checks a criterion based on its complete neighborhoodwhen the Blackbone2 algorithm consider two different setsof neighbors (backbone and non-backbone). These two setsare more frequently likely to change during the simulationtime than the complete set of neighbors and thus the Black-bone2 algorithm will induce more state changes. The samereason explains the better performances of the two variants:high degree and forced stability. In these two cases, somenodes are temporarily fixed into a previous state based on aparticular condition.

The forced stability variant obtains the best results ifwe consider Blackbone2 variants only. However, its perfor-mances mainly depend on the value of its parameter. Figures7 and 8 show that the state changes are also dependent ofthe speed of the nodes. However the Dai and Wu algorithmis characterized by a slow and almost linear increasing whenthe Blackbone variants suffer from a high rise as soon as themobility appears.

5.3.3 AvailabilityThe availability criterion is composed of two different mea-

sures: the connected component ratio and the number ofisolated nodes. Our results show that these two measuresare antagonist in most of the cases: a worse cover of thenon-backbone nodes may induce a better ratio.

Fig. 9 and 10 summarize the performances concerningisolated nodes in the low robustness case. The results arealmost identical in the more robust case. From these twofigures we can conclude that the Blackbone2 variants ob-tain significantly better results than the Dai and Wu algo-rithm. Indeed, the Blackbone2 variants remain stable in-dependently of the size of the network or the speed of thenodes. Dai and Wu algorithm on the contrary, shows veryfluctuant results depending on the simulation run. This isparticularly surprising considering the bigger size of its gen-erated backbones.

However, the results are completely different concerningthe connected components ratio. In Fig. 11 and 12 we cansee that the Blackbone2 variants obtains a decreasing ratiowhen the density or the speed increase. These results canbe explained by the increasing number of state changes re-quired when these two parameters are increased. The Daiand Wu algorithm shows very good results independentlyof the context: the ratio stays above 1. These good resultscan however be partially explained by the poor results con-cerning the isolated nodes. Moreover, values above 1 can beconsidered a lack of adaptability as the algorithm may nothave adapted itself quick enough to the topology changes.This low-adaptability characteristic is also explains the highcount of isolated nodes.

5.4 Performance comparison summaryIn a random mobility context we can conclude that the

technique of reducing the considered neighborhood does nothelp achieve better quality solutions. It is however possiblethat the results would be completely different with more re-alistic mobility models in which groups of nodes are movingin the same directions (e.g. cars on highways or city street,pedestrian in urban streets).

27

The high degree variant produces almost the same com-pact backbones than the genuine algorithm but increases thestability. Its performances for the other quality measures arealso very close to those of the original version. The absenceof trade-off induces that this variant should be considered areplacement for the original algorithm.

The forced stability version of the Blackbone2 algorithmis the variant that benefits from the best stability. Evenif the backbone size overhead with this technique exists, itcan still be considered a good solution when a more stablebackbone is required. Moreover, as all Blackbone2 variants,its theoretical computation time, O(∆2) [13], allows it to bedeployed on a wide panel of devices. However, even thoughthis variant obtained the best stability results among theother variant, its stability performances are still far belowthose of the Dai and Wu algorithm.

The Dai and Wu algorithm obtains impressive results con-cerning the stability of the backbone and the connected com-ponent ratio. However this algorithm may not be suitablein dense networks for two reasons. First, the size of thegenerated backbone is bigger than those of the Blackbone2variants in most of the cases. Second, the theoretical com-putation time is very high, O(k∆4), with ∆ the averagedensity, which may be a problem with not powerful devices.

6. CONCLUSIONIn this paper we proposed different measures and criteria

to quantify the quality of a backbone in a mobile context.These measures are a set of indicators that may be usedin order to have a better understanding of the raw perfor-mances of different decentralized algorithms designed to cre-ate k, m−CDS based virtual backbone. The study of theseperformances may be a useful tool to choose an algorithmthat suits specific needs that may appear in real implemen-tation contexts. Different variants of the genuine Blackbone2 algorithm have also been tested in order to increase theperformances for some often overlooked or forgotten qualitycriteria. Blackbone 2 variants obtain very promising resultsin terms of size and availability and the Dai and Wu algo-rithm creates very stable backbones. As these results havebeen obtained on a discrete event-based simulator, an in-teresting future work would be to test the quality of thesedifferent algorithms in a discrete time simulator, in orderto have an idea of the algorithms complexity impact on thegenerated solutions.

7. REFERENCES[1] C. Adjih, E. Baccelli, T. Clausen, and P. Jacquet. On

the robustness and stability of connected dominatingsets. Rapport de recherche 5609, INRIA, sept 1997.

[2] K. M. Alzoubi, P.-J. Wan, and O. Frieder. Newdistributed algorithm for connected dominating set inwireless ad hoc networks. Proc. IEEE Hawaii Intl.Conf. System Sciences, 2002.

[3] S. Basagni, M. Mastrogiovanni, A. Panconesi, andC. Petrioli. Localized protocols for ad hoc clusteringand backbone formation: A performance comparison.IEEE Transactions on Parallel and DistributedSystems, 17(4):292–306, 4 2006.

[4] B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unitdisk graphs. Discrete Mathematics, 86(1-3):165–177,1990.

[5] F. Dai and J. Wu. An extended localized algorithm forconnected dominating set formation in ad hoc wirelessnetworks. IEEE Trans. Parallel and DistributedSystems, 15(10):908–920, 10 2004.

[6] F. Dai and J. Wu. On constructing k-connectedk-dominating set in wireless network. IEEEInternational Parallel and Distributed ProcessingSymposium, 2005.

[7] D.-Z. Du and P. Pardalos. Handbook of CombinatorialOptimization. Kluwer Academic Publishers, 2004.

[8] P. Gupta and P.R. Kumar. The capacity of wirelessnetworks. IEEE Transactions on Information Theory,IT-46(3):388–404, 2000.

[9] D. Kim, Y. Wu, Y. Li, F. Zou, and D.-Zhu Du.Constructing energy efficient connected dominatingsets with bounded diameters in wireless networks.IEEE Transactions on Parallel and DistributedSystems, 2007.

[10] Y. Li, S. Zhu, My T. Thai, and D.-Z. Du. Localizedconstruction of connected dominatinf set in wirelessnetworks. IEEE INFOCOM, 2002.

[11] Y. Pigne. Modelling and decentralized processing ofdynamic graphs - application to mobile ad hocnetworks. PhD thesis, University of Le Havres, dec2008.

[12] J. Schleich, P. Bouvry, and Le Thi Hoai An.Decentralized fault-tolerant connected dominating setalgorithm for mobile ad hoc networks. In InternationalConference on Wireless Networks, 2009.

[13] J. Schleich, P. Bouvry, G. Danoy, and Le Thi Hoai An.Blackbone2, an efficient deterministic algorithm forcreating 2-connected m-dominating set-basedbackbones in ad hoc networks. In Proc. 7th ACMInternational Symposium on Mobility Managementand Wireless Access, 2009.

[14] W. Shang, F. Yao, P. Wan, and X. Hu. Algorithms forminimum m-connected k-dominating set problem.COCOA 2007, LNCS 4616, pages 182–190, 2007.

[15] F. Wang, M. T. Thai, and D.-Z. Du. 2-connectedvirtual backbone in wireless network. Accepted byIEEE Transactions on Wireless Communication, 2007.

[16] Y. Wang, W. Wang, and W. Y. Li. Efficientdistributed low-cost backbone formation for wirelessnetworks. IEEE Transactions on Parallel andDistributed Systems, 17(7):681–693, 7 2006.

[17] J. Wu. An enhanced approach to determine a smallforward node set based on multi-point relay. Proc.58th IEEE Semiann. Vehicular Technology Conf,4:2774–2777, 10 2003.

[18] J. Wu and H. Li. On calculating connecteddominating sets for efficient routing in ad hoc wirelessnetworks. Proc. Third ACM Int’l Workshop DiscreteAlgorithms and Methods for Mobile Computing andComm., Dial M 1999:7–17, 8 1999.

[19] Y. Wu, F. Wang, M. T. Thai, and Y. Li. Constructingk-connected m-dominating sets in wireless sensornetworks. Military Communication Conference, 102007.

[20] Y. Wu and Y. Li. Construction algorithms fork-connected m-dominating sets in wireless sensornetworks. Mobihoc’08, pages 83–90, 5 2008.

28

[acm press the 8th acm international workshop - bodrum, turkey (2010.10.17-2010.10.18)] proceedings...

Documents