Cluster Mesh Based Multicast Routing in MANET - Semantic Scholar

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Cluster Mesh Based Multicast Routing in MANET: An Analytical Study Mohamed Younis*, Osama Farrag**, and Sookyoung Lee* *

Dept. of Computer Science and Electrical Engineering, University of Maryland Baltimore County Baltimore, Maryland, USA ** The Johns Hopkins University, Applied Physics Lab., Laurel, Maryland, USA

Abstract— Multicast streams are the most popular traffic pattern in many applications of mobile ad-hoc networks (MANET). However, the mobility of nodes causes frequent changes to the network topology and thus efficient routing of multicast traffic becomes very challenging. The establishment of a core-mesh has been deemed as a very effective solution for these dynamic setups. The core-mesh acts as a backbone in order to avoid frequent route discovery. However maintaining the core-mesh imposes significant overhead that dominates the performance for large networks. This paper advocates a novel methodology that combines network clustering and mesh-based multicast routing. The Cluster-Mesh based Multicast Routing (CMMR) methodology forms a backbone using cluster-heads. This makes the backbone more stable against frequent node mobility and enables scalability by limiting the scope of the core maintenance. The paper mainly captures the performance advantage of CMMR over contemporary node-based core-mesh strategies. A mathematical model is developed to analyze the average performance of one of the contemporary core-mesh routing schemes and an implementation of the CMMR methodology using the same mesh formation algorithm. The numerical results demonstrate the advantage of CMMR.

I. INTRODUCTION Ad-hoc networking of mobile nodes has received lots of attention from practitioners and the research community in recent years. The interest has been fueled by numerous applications such as combat field coordination among troops, disaster management, road safety, etc. Unfortunately, lack of a viable multicast routing strategy that can scale to a large number of nodes, large number of sessions, and long multi-hops paths remains a primary factor limiting wide deployments of MANET. In MANET node mobility causes frequent changes to the network topology and imposes major overhead for route setup and maintenance. The overhead is mainly related to the control traffic required for topology management and causes the wastage of bandwidth and onboard energy. Such overhead motivated the development of numerous routing protocols for the efficient dissemination of multicast streams [1][2]. In many large scale MANET applications, the network is required to support a large number of multicast sessions, with diverse source and destinations multicast groups; moreover, many multicast sessions are short-lived. Therefore, establishing a core-assisted mesh will be the most suitable strategy in such a case given the frequent changes in the topology caused by node mobility. The core nodes play the role of a backbone of a routing topology. Multicast traffic can be routed from a source to the closest core node and then forwarded to the destinations. Examples of core-assisted mesh protocols include MCEDAR [3], CAMP [4], PAST-DM [5] and SRMP [6]. The obvious

advantage of this approach is that route discovery would be infrequent since a source has only to reach the closest core node on the mesh. However, maintaining the core-mesh involves significant messaging overhead in order to ensure that the core nodes are connected to each other and that all destinations can be reached from at least one node in the core. The maintenance cost grows in a highly dynamic environment due to frequent changes in nodes location, and thus contemporary node-based core-mesh approaches do not scale well for networks with long paths and large node populations. This paper prompts a novel Cluster-Mesh based Multicast Routing (CMMR) methodology. CMMR opts to support scalability and robustness by grouping nodes into link-layer clusters and forming a backbone using cluster-heads. The main idea is that cluster-based mesh is more stable than a node-based mesh since the cluster topology is less likely to change when a node moves to a different location. In addition, the effect of changing the route from a core node to a source or to a receiver of a multicast packet will be, in most cases, local to the cluster and will not have to involve all mesh members. This paper presents an analytical performance model for CMMR and demonstrates its advantage over node-based core mesh approaches. In particular, the multicast core extraction distributed ad hoc routing (MCEDAR) algorithm [3] is used as a baseline. An implementation of CMMR using the mesh formation algorithm of MCEDAR is pursued and overhead estimates are derived. The numerical results confirm the advantage of CMMR and highlight the characteristics of MANET for which employing the CMMR methodology makes sense. II. CMMR OVERVIEW The fundamental design principle of the core-mesh approach for multicast routing is to form a relatively stable backbone that can be referred to when disseminating a multicast packet to destinations. The core-mesh is formed by finding a connected dominating set among the network nodes. A source routes a packet to the closest core node in order to be forwarded to all members of the multicast group, which can be on the core itself or dominatees that can be reached from the core. While using the core-mesh will significantly cut the route discovery overhead, maintaining the mesh incurs messaging overhead. The maintenance overhead grows with the network size and is incurred when the network topology changes. Thus, in large and highly dynamic MANET applications frequent node mobility may nullify the advantage of the core-mesh and deem it as an ineffective multicast routing methodology.

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Figure 1: CMMR forms a dominating set of communicating clusters that serves as a backbone for routing multicast traffic

CMMR opts to counter the maintenance cost and boost the stability of the routing backbone. The main idea is to form a mesh on the level of clusters rather than individual nodes. Figure 1 shows an articulation of the concept. Grouping nodes into clusters has been deemed as an effective means for achieving scalability [7]. Multi-hop clustering is generally categorized based on the cluster radius “k”. While a large cluster radius makes the cluster topology more stable, increasing k boosts the overhead in cluster maintenance. Cluster formation techniques, whether centralized or distributed, designate a lead node for each cluster that is often referred to as cluster-head (CH). Two clusters i and j are said to be adjacent if there is a path between CHi and CHj that does not involve any node outside these two clusters. Like the node-based core, CMMR forms a cluster-adjancy graph and uses it to identify a connected dominating set. Dominating clusters serve as an inter-cluster backbone for facilitating multicast. Intra-cluster routing is localized using the algorithm of choice. Inter-cluster traffic goes through the dominating set of clusters. A source will reach local recipients, i.e., those belonging to its cluster, through intra-cluster paths and send the multicast packet to the closest CH on the cluster mesh. The multicast packet will then be disseminated to all CHs on the mesh to be forwarded to recipients within the dominating clusters and to the CH of leaf (dominatee) clusters. Given the cluster-level management of data routes, the motion of most individual nodes will have a mostly local effect and would have minimal impact on the multicast traffic, if any. Since the focus of this paper is on assessing the advantage of CMMR over the node-based core-mesh methodology, the mesh formation procedure of the baseline approach MCEDAR is applied to CMMR in order to mute the effect of the dominating set algorithm on the results. III. ANALYTICAL PERFORMANCE ESTIMATES This section analytically compares the performance of the CMMR methodology to MCEDAR [3], which is one of the popular node-based core mesh schemes. The messaging overhead for CMMR and the baseline approach is analyzed in the following subsections.

A. Mesh Formation Analysis Assume that the network consists of N nodes that are uniformly spread in an area of interest. To form a mesh in MCEDAR, the messaging complexity is N[2 + (4d-1)λ] where λ is the fraction of the node count that becomes part of the core. Basically, each node broadcasts a message at the beginning indicating its degree, i.e., N messages overall. The node with the highest degree, i.e., most connectivity, in its neighborhood becomes a dominator. Each dominatee elects and notifies its dominator, i.e., a total of (N-|core|) = N(1-λ) messages. Finally each core member announces itself to up to 3-hop neighbors. For a uniform node distribution the average number of nodes up to k-hop neighbors is estimated to be dk2 [8], where d is the average node degree in the network, and hence a core member announcement will involve (3 1) = 4d messages. Thus the total number of messages is N+ N(1-λ) +4dλN = N[2 + (4d-1)λ]. The maintenance of the mesh in MCEDAR is done by simply running the formation algorithm periodically. The analytical performance estimates for CMMR are based on the following assumptions: • The radius of a cluster can be approximated by a circle with radius = kR, where R is the radio range of a node. • The cluster-head is located at the center of the cluster. Based on these assumptions, it has been shown in [8] that a khop cluster would have an average number of nodes per cluster, = and an average number of clusters = . The average number of transmissions to flood a message until reaching all k-hop neighbors of a node can be estimated as the average number of non-leaf nodes in a breadth-first ordering of a graph rooted at the sender, i.e., the number of nodes for up to (k1) hops, which would equal the average node count in a (k-1)hop cluster, i.e., ( 1) . For CMMR, grouping nodes into clusters is performed by having NCH nodes broadcasting self-nomination messages that reach up to k hops from these individual nodes. Assuming a selfnomination message will be disseminated through broadcast, the total message count for all nomination traffic is ( 1) . Assuming membership confirmations are aggregated so that each cluster member transmits only once, (N – NCH) messages will be sent by non-self-nominated nodes to declare their association with one cluster-head. Similar to MCEDAR, the CMMR cluster-mesh can be formed by substituting N with NCH and factoring in the path length between cluster-heads, which is 2k. Thus, the messaging complexity of cluster-mesh [2 + (4 1)α], where α is the formation is 2 percentage of clusters in the core. Considering all steps, the total number of messages for establishing cluster-mesh in CMMR is: MessageCMMR = ( 1)α] (4

Replacing ( members ( =( (4

)+

(

1)

+2

[2 +

) with the estimated number of cluster 1) 1) 1)α]

+

(

1)

+2

[2 +


=

([2

2

1] + 2 [2 + (4

+

1)α])

B. Maintenance overhead analysis Assume a link failure rate of δ due to the mobility of a node. We estimate the impact on the multicast routing topology and the overhead for maintaining the routes as follows: • MCEDAR: The formation procedure is repeated periodically in order to update the mesh. Thus, the maintenance overhead is N[2 + (4d-1)λ]. • CMMR: The failed link may cause: a. A node to depart its current cluster and either (i) move to another cluster, or (ii) form a new cluster (update the core mesh) b. A CH to become unreachable to its cluster members c. No change in the network topology, meaning the cluster memberships stay intact and the current inter-cluster connectivity remains the same. Therefore, for CMMR we estimate the probability of each of the above scenarios and assess the average messaging cost for cluster-mesh maintenance accordingly. The analysis below approximates a k-hop cluster with a circle of radius k. 1. A member node departs forming a new distinct cluster. The incurred overhead in this case will be 2k × 2 messages in order for the new cluster-head to hook up with the cluster-mesh (to inform two neighboring clusters on the mesh). The probability ( ) Ψ, based on the following of this happening is about derivation: • Assume a circular cluster, the number of nodes in the cluster is dk2 and the number of periphery nodes in the cluster = dk2 – d(k-1)2 = d(2k-1). The probability that one of them (

)

moves out and departs the cluster would be . It should be noted that this probability can be derived in a similar way by noticing that d(2k-1)×NCH out of the N nodes fit this case making the probability of edge node movement =

(

)

=

(

)

.

• The term Ψ captures the probability that the node moves to an area that is outside the coverage of all clusters and is multiplied in order to capture the effect of having no neighboring clusters. The uncovered area can be estimated as

∑

=

communication Ψ=

1

(

range )

,

(

)

, where R is the

of (

a )

node.

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1

0, 2. A member node moves to a neighboring cluster. The messaging overhead in this case will be 2k to inform the heads of the old and new clusters. The probability of this happening ( ) (1 Ψ), based on the derivation of the first is about case above. 3. A CH abandons its cluster members. This happens when the CH is on the boundary of the cluster (skewed cluster). The members of the clusters become orphaned in this case while

the departing CH is handled by cases (1) and (2) above. Generally, one of the 1-hop neighbors will become a clusterhead and lead the orphaned nodes. The probability for this to based on a semicircular cluster with the CH happen is positioned at the center. The number of messages for the new CH to regroup the orphaned nodes will be (½ dk2-1) since there are fewer nodes than a circular cluster. Also (2k × dCH) messages are needed to update neighboring members on the cluster-mesh. The average number of messages to handle changes in the topology caused by the departure of a member from a cluster, i.e., cases 1 and 2 above, is: (

MessagesMember = 4 =

(

) )

(

Ψ+ 2

)

(1

Ψ)

(1 + Ψ)

When the change is due to the departure of a CH, case 3, the average number of required messages is: MessagesCH =

1 + (2

)+ 4

Ψ+2

1 + (2

)+ 2

(1 + Ψ)

(1

Ψ) =

Aggregating MessagesMember and MessagesCH, the average number of messages for maintaining the cluster-mesh is: (

)

1 + (2

= Where Ψ =

)+ 2

1 + (2

MessagesCMMR =

,

1

(1 + Ψ) +

(1 + Ψ) (

+

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(1 + Ψ)

1

0,

C. Multicast overhead analysis In MCEDAR multicast packets are forwarded within the mesh on a tree. Assuming a reasonable node degree and relatively large multicast group, 50% of the nodes may be involved on the average in intra-mesh forwarding. Dominatee nodes in the network which are also members of the multicast group are assumed to represent a fraction β of the overall group size m. Given the approximation of the intra-mesh transmissions, the value of β should ensure that (1-β)m ≤ ½ N (given the involvement of 50% of the nodes in the intra-mesh forwarding). Meanwhile, in CMMR a multicast will consists of the following 3 steps: 1. Go to the core: the source will try to the reach the head of the parent cluster, which is a member of the core. In the worst case, a source S will have to send the multicast message to its local cluster-head CHs over k hops. CHs will reach CHi of the parent cluster that serves on the core mesh over a 2k-hop path. In other words, to reach the closest CH on the core mesh from a source, it takes at most 3k transmissions. 2. Broadcast within the core: CHi, which has just received the multicast from node S, will broadcast it to the heads of all clusters that are member of the core.


3. Deliver to destination clusters/nodes: Since the multicast group members may be scattered throughout the network, the multicast packet would need to be sent to some leaf clusters as well as to nodes in the clusters of the core mesh. Suppose that there are m members in a multicast group and the number of clusters in the mesh is a fraction α of the number of clusters in the network. Assuming that the m nodes are evenly distributed over all clusters, a fraction α of the m nodes will be in the core clusters and (1-α) will be in leaf clusters. The number of transmissions in CMMR = 3k + 2k × (|Core|-1) + 3k × (1- α) m + k × α m = 3k + 2k × (αNCH - 1) + k × (3-2α) m Table 1 summarizes the message complexity of the CMMR and the baseline approach. Table 1: Comparison of the analytical performance estimates for CMMR and the baseline approach Messaging complexity

MCEDAR

Formation

N[2 + (4d-1)λ]

CMMR [2 2 + +2 [2 + (4 2

Maintenance

N[2 + (4d-1)λ] +

Packet delivery (m receivers)

1 2 4 + 2 (2

1] 1)α]

1 + (2 1)

(1 + Ψ)

3k + 2k × (αNCH - 1) + k × (3-2α)m

½ N + βm

D. Estimating the node and Cluster degree “dCH” Assume nodes distribution in the deployment area obeys a uniform random distribution. For a network size of N nodes, the probability for a node j to have q neighbors. i.e., there are q nodes within the communication range R of node j, can be calculated using the binomial distribution as: ( )=

(1

)

,

Where p is the probability that a node has a link to, i.e., lies inside the communication range of, another node, Thus, p can be defined as:

=

The average node degree “d” in the network can be calculated as the expected value for P: = ( )=

=

=

,

Where is the node density in the network. Modeling a cluster as a circle of radius k hops, the path length between the heads of two adjacent clusters would be 2k hops. Assuming a uniform distribution of nodes, the clusters at the inner part of the deployment area will have a layout as shown in Figure 2. Since two clusters are adjacent if their heads are 2k hop neighbors, the position of the CH neighbors of CHi will be on the circumference of a circle of radius 2k with the

Figure 2: With a uniform cluster density, the cluster-head neighbors of CHi will be evenly placed on the circumference of a circle of radius 2kR with a distance of 2kR between every two CH in a row. This makes them vertices of a hexagon and thus the cluster-degree is 6.

node CHi positioned at the center. In addition, those cluster-head neighbors, e.g. CHa andCHb, may belong to adjacent clusters themselves and would have a 2k hop distance between them. Based on this model of the inter-cluster connectivity, a cluster will have at most 6 neighbors. Such cluster-degree will be lower at the boundary of a rectangular deployment area. Nonetheless, for a cluster-mesh it is reasonable to assume a cluster-degree of 6 for the clusters that are part of the core since they represent a connected dominating set and are not thus expected to have a cluster that is close to the boundary of the deployment area. IV. NUMERICAL RESULTS This section shows some numerical results based on the analysis in the previous section. Again the performance metric is the total number of transmissions (delivery cost) per multicast packet. In addition to comparing to MCEDAR, the goal is to articulate the effect of the various parameters on the performance of CMMR and highlight how a suitable configuration can be picked. We compare the overhead for forming the routing topology. The performance under node mobility is also captured. In all graphs, it is assumed that the communication range is 100 m and that the network is deployed in 1000m × 1000m area. It is worth noting that the effect of the radio ranges on the maintenance cost is very minimal and is not plotted. To factor in the effect of mobility on the performance, we assume that links fail at a rate η per multicast packets generated by the source. This models how dynamic the nodes are and how frequent the source generates multicast packets. While the link failure rate is often modeled as occurrence per time unit, a broken link will only impact the routing topology when a packet is transmitted. Thus, the definition of η would suit the use of number of transmissions as a performance metric. The aggregate performance under node mobility conditions is estimated as follows: Aggregate performance = η × Maintenance cost + multicast cost


Formation and maintenance: Figure 3 showss the number of messages required to form the routing topologgy with both the core size α (for CMMR) and λ (for MCEDAR) are set to 30% of the clusters and nodes, respectively. Overall, tthe overhead for forming the routing topology grows in proportioon to the number of nodes as indicated in Table 1 above. Overall the increased connectivity boosts the messaging overhead tto form the core mesh in MCEDAR. For CMMR, the ooverhead drops significantly when d and k increase. Although suuch a drop seems to contradict the formula in Table 1, wheree the messaging overhead for forming the mesh grows with k and to a lesser degree with d, the estimated number of clusterss NCH is inversely proportional to d and k2 which causes the overhhead to decrease. Overall, for networks with similar average nnode degree the overhead for forming the cluster-mesh in CMM MR is lower than that for the core-mesh in MCEDAR. In additioon, the overhead for maintaining the multicast routing topologyy for MCEDAR significantly surpasses that of CMMR. Figure 4 shows that the maintenance overhead for CMMR is negligiblee when compared to that of MCEDAR. Multicast routing performance: Figure 5 plotss the number of messages needed for all 100 members in a m multicast group to receive a packet sent by a source in a stationaryy network, i.e., η =0. The assumed values of α, β and λ are 30% %, 50% and 30%, respectively. While for small networks MCEDA AR yields distinct

performance, CMMR does very weell in large networks. Overall, the performance of CMMR is almo ost flat regardless the network size. However, the cluster radius k is very influential. As shown in Figure 5, changing k from 2 to 3 boosts the packet count by nnectivity, i.e. higher d, has a about 25%. Increased network con positive effect on CMMR. Effect of multicast group size: Fig gure 6 compares the delivery cost for a multicast packet to a group of 100, 250 and 500 mobile nodes. The figure indicattes that the performance of CMMR is linear in the network siize. CMMR performs at best for small multicast groups. However, for big networks, CMMR outperforms MCEDAR even for laarge multicast groups. This is mainly attributed to the topology management m overhead which CMMR could avoid through the cluster-mesh structure. It is worth noting that increasing η, which w reflects high level of mobility, makes the performance of o CMMR very dominant, as will be shown later. Effect of the number of multicast groups: g Figure 7 studies how the number of active multicast gro oups affects the performance. This is not similar to having a largee multicast group since every multicast session will have its own o routes. Two plots are provided for different numbers off members per the individual MMR continues to yield good groups. Figure 7 indicates that CM performance and stays superior to MCEDAR M for large networks. The performance advantage of CMMR even grows with the

Figure 3: Comparing the messaging overhead Figgure 4: CMMR introduces minimal, and very Figure 5: Thee number of messages required to ket to a multicast group of 100 for forming the routing topology under CMMR, neggligible maintenance overhead compared to deliver a pack MC CEDAR (α=λ=0.3). nodes (α=λ=0.3, β=0.5 and η =0) and MCEDAR (α=λ=0.3).

(a) (b) Figure 6: Performance under varying network Figgure 7: Capturing how the existence of multiple multicast groups g would impact the overall and multicast group sizes (α=λ=0.3, β=0.5, perrformance (α=λ=0.3, β=0.5, and = η 1/10). The multicast group ps have 100 nodes in (a) and 250 in (b). k=2, d=3, and η = 1/10).


increase in the number of active multicast grroups. For small networks MCEDAR still has an edge for big muulticast groups. Effect of the core size: Figure 8 studies the impact of the size of the core mesh, in terms of the percentage of the number of nodes R respectively, on (λ) and clusters (α) for MCEDAR and CMMR the performance. The plot indicates that a smaaller core mesh is better for MCEDAR while a large core boosts the performance of CMMR. CMMR seems to have a great advvantage for large cores (α=λ=70%). It is worth noting that the core mesh is in fact a connected dominating set and thus the ssize of the mesh grows with the node degree in the network [[9]. As indicated earlier the node degree is proportional to thee communication range and node density, and thus λ may be large in practice causing the performance of MCEDAR to sufffer. On the other hand, increasing the size of the core is beneficiaal for CMMR and the increased network connectivity would hhave a positive impact. Effect of link failure rate: Figure 9 highlightts the impact of increased mobility on the delivery cost for a m multicast packet. The effect of mobility is modeled as the frrequency of link failures per generated multicast packets. Figuree 6 indicates that in a highly dynamic network, CMMR yieldds very distinct performances for all network sizes. In fact, C CMMR does not seem to be affected by node mobility (all CMMR curves overlap) given its relatively small mesh mainteenance overhead. When links fail at lower rates, MCEDAR pperforms slightly better than CMMR for small networks. Session length considerations: Figures 6-9 stuudy the effect of mobility based on a single multicast packet andd do not factor in the cost of forming the routing infrastructuure. One of the important design decisions is whether the lengthh of the session is a factor in determining the most suitable apprroach. Figure 10 opts to address this point by plotting the overrall performance while including the session length measured in terms of the multicast sessions, number of generated packets. While for short m the difference in performance is not much, lonng sessions incur significant topology maintenance overhead m making CMMR a favorable choice, especially under frequent link failures.

USION V. CONCLU

This paper has presented CMMR, a novel cluster-mesh based g in MANET. The idea is to methodology for multicast routing form a relatively stable backbo one in a highly dynamic environment. Nodes are grou uped into clusters. Cluster adjacency is modeled as a graph an nd a connected dominating set is identified to serve as a core. Mu ulticast traffic is routed to the closest cluster-head on the core in i order to be disseminated throughout the core and forwarded d locally to recipients by the head of their individual clusters. The paper has focused on making the case for CMMR by comparing it to one of the cotemporary node-based core-assiisted mesh protocols. The numerical results have demonstrated the advantage of CMMR in efficiently supporting large networrks and boosting the stability of the routing topology. The resu ults have also highlighted the impact of the various parametters in order to facilitate performance tuning. NCES REFEREN [1] X. Chen and J. Wu, “Multicasting techn niques in mobile ad-hoc networks,” in the Handbook of Ad-hoc Wireless Netw works, M. Ilyas and R. C. Dorf, Eds., CRC Press, Boca Raton, FL, pp. 25–40, 2003. [2] L. Junhai; Y. Danxia; X. Liu and F. Min ngyu, “A survey of multicast routing protocols for mobile Ad-Hoc networks,” IEEE Comm. Surveys & Tutorials, 11(1), pp.78-91, First Quarter 2009. [3] P. Sinham, R. Sivakumar and V. Bharg ghavan, “MCEDAR: Multicast CoreExtraction Distributed Ad hoc Routing g,” Proc. the Wireless Comm. and Networking Conf. (WCNC'99), New Orleeans, LA, September 1999. [4] J. J. Garcia-Luna-Aceves, and E. L. Madruga M “The Core-Assisted Mesh Protocol,” IEEE J. on Sel. Areas in Com mm., 17(8):1380-1394, Aug 1999. [5] C. Gui and P. Mohapatra, “Overlay mu ulticast for MANETs using dynamic virtual mesh,” Wireless Networks, Vol. 13, 1 No. 1, pp. 77 - 91, Jan 2007. [6] H. Moustafa and H. Labiod: "SRMP: A Mesh-based Protocol for Multicast Communication in ad hoc networks", Proc. P the Int’l Conf. on Third Gen. Wireless and Beyond, San Francisco, CA A, May 2002. [7] J.Y. Yu, and P.H.J. Chong , “A survey of clustering schemes for mobile ad hoc networks,” IEEE Communications Surveys S & Tutorials, ,7(1), pp.32-48, First Qtr. 2005. [8] M. Youssef, A. Youssef and M. Youniss, “Overlapping Multihop Clustering for Wireless Sensor Networks,” IEEE Trans. on Parallel and Distributed systems, 20(12), pp. 1844-1856, Decemb ber 2009. [9] A.T.J., Blum, M. Ding, and X. Chen ng, “Connected Dominating Set in Sensor Networks and MANETs,” book chapter, Handbook of Combinatorial Optimization, D.-Z. Du, and P. Pard dalos (eds.), pp. 329–369, Kluwer Academic Publishers, Dordrecht, 2004.

Figure 8: How the size of the core mesh affects Fiigure 9: How the link failure rate impacts the Figure 10: Peerformance while factoring the the performance of CMMR and MCEDAR nuumber of transmissions per multicast packet overhead forr the routing infrastructure (β=0.5 and η = 1/10). (α α=λ=0.3, β=0.5, and m=100). (α=λ=0.3, β=0 0.5, m=100, and η = 1/10)