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Multicast in Wireless Mesh Network Xuan (William) Zhang Xun Shi

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2006/11/072 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/073 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/074 What is Multicast? “Point-to-multipoint" or "multipoint-to- multipoint“ Different from broadcast and unicast (a) Broadcast(b) Multicast(c) Unicast

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2006/11/075 Advantages of Multicast Delivery to destinations simultaneously Deliver the messages over each link of the network only once Only create copies when the links to the destinations split

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2006/11/076 Wireless Mesh Networks Mesh routers are generally stationary Multi-hop forwarding High speed Reliable power supply

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2006/11/077 Internet multicast protocols Feature Wired / Powerful / Reliable Maintain a large and fixed topology Shortest path algorithms simpler to implement simpler to support frequent joins/leaves lowest delay

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2006/11/078 Drawbacks of Internet multicast in WMNs Routing metrics do not aim at minimizing the cost of multicast tree Not using broadcast nature

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2006/11/079 MANET multicast protocols Feature Maintaining a smaller and mobility network topology Relying on flooding mechanism On-demand routing protocols Suitable for mobility Low power consumption

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2006/11/0710 Drawbacks of MANET multicast in WMNs Complexity of computation High mobility High Power consumption

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2006/11/0711 Multicast protocols in WMNs WMNs multicast is between Internet and MANET multicast Fixed topology Broadcast nature Mobility and power are not problems

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2006/11/0712 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/0713 Traditional definition of cost Measured by hops, delays, etc. Minimum Steiner tree problem NP-complete Heuristic algorithms – polynomial time Shortest path tree Sub-optimal shared tree MST algorithm: 2*optimal approximation Zelikovsky algorithm: 11/6*optimal approximation

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2006/11/0714 Define the cost in WMNs Cost: number of transmissions Minimize the number of transmissions Maximize the forwarding nodes which are shared by sender-receiver paths This problem is NP-complete

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2006/11/0715 Problem with Steiner Tree Steiner Tree: minimum edge cost Broadcast: node can send neighbors data in one transmission Our goal: minimizing the number of transmissions!!

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2006/11/0716 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/0717 Ruiz ’ s Algorithm Purpose: find minimal data overhead tree Contributions: Theorem 1: Prove Steiner tree is not optimal in WMNs with respect to the number of transmissions Theorem 2: Prove minimal data overhead tree is NP-Complete Proposed heuristics to compute trees with minimizing the number of transmissions

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2006/11/0718 Problem statement Define t is multicast delivery tree Define Ct(t) is the number of transmissions required to deliver a message from sender s to receiver set R Problem statement: Minimize the Ct(t) Ct(t)=1+|Ft| Minimize the number of forwarding nodes

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2006/11/0719 Theorem 1: Steiner tree not minimal Steiner multicast tree (minimal edge cost) is not the minimal data-overhead multicast tree. Proof by example:

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2006/11/0720 Theorem 2: NP-Complete Proof by including a particular case Special case: R=V-{s}, find the smallest forwarding nodes covers the rest of nodes in V-{s} Vertex cover problem – NP-complete

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2006/11/0721 Heuristic Algorithm Goal: approximate minimal data overhead multicast tree Reduce the number of forwarding nodes While increase the number of leaf nodes Centralized greedy-based heuristic algorithm Distributed heuristic algorithm

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2006/11/0722 Greedy minimal data overhead Alg. Centralized WMNs Greedily build cost-effective sub-trees A node v is selected a forwarding node only if it covers two or more nodes

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2006/11/0723 Greedy minimal data overhead Alg. cont. Steps Construct a cost- efficient sub-trees Build a Steiner tree among the roots of the sub- trees

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2006/11/0724 Initialize V=V-{s} aux=R-Con(s)+{s} empty Alg Demo ε MF (multicast forward node list) M1, R1, R2, R3, R4, R5, R6 V (unvisited nodes) aux (nodes to cover list) M2, M3, M1, R1, R2, R3, R4, R5, R6 M2 S, R5, R6, M2 M3 S R1 R2 R3 R4 R5 M2M1 M3 R6 S, M2, M3 M2, M3 Loop V=V-v MF=MF+{v} aux=aux-Cov(v)+{v} M3, M1, R1, R2, R3, R4, R5, R6 S, R2, R3, R4, R5, R6, M2 S R1 R2 R3 R4 R5 M2M1 M3 R6 S R1 R2 R3 R4 R5 M2M1 M3 R6 Stop!! All nodes in V now only cover at most 1 receiver S R1 R2 R3 R4 R5 M2M1 M3 R6 MST heuristics to build Steiner tree S R1 R2 R3 R4 R5 M2M1 M3 R6 minimal data overhead tree! Hehe!!

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2006/11/0725 Performance Evaluation Compared Algs SPT: source path tree Alg MST: Steiner tree Alg MNT: centralized proposed Alg MNT2: distributed proposed Alg Simulations Number of Tx required Mean number of hops Number of Tx with density

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2006/11/0726 Performance Evaluation cont. Number of transmissions required The total number of packets transmitted either by the source or any relay node in path. MNT, MNT2 MST SPT Theorem 2, Steiner tree is not minimum data-overhead. Do not aim at minimize the cost of the tree.

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2006/11/0727 Performance Evaluation cont. Mean path length (Mean number of hops) The number of multicast hops from a receiver to the source averaged over the total number of receivers. MNT, MNT2 MST SPT Aim at minimize the length of the tree.

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2006/11/0728 Performance Evaluation cont. Number of transmissions with density Examine reduction of Tx numbers when increase the density. Proposed heuristic MNT, MNT2 reduced more than SPT and MST!

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2006/11/0729 Summary of Ruiz ’ s Algorithm Steiner tree does not suitable in WMNs The proposed Algorithm is NP-complete Heuristic Algorithm Centralized Algorithm Distributed Algorithm Evaluation the higher the density, the higher are the Heuristic Alg performance

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2006/11/0730 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/0731 Resilient Forwarding Mesh Makes multicast robust to node or link failure 2 paths Increases PDR and throughput

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2006/11/0732 Resilient Forwarding Mesh Example (a) Network topology (b) Optimal solution (c) Suboptimal solution

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2006/11/0733 Node-Disjoint Paths Parallel routes that connect the source and the destination Do not have any node in common except the source and destination Deliver packets simultaneously

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2006/11/0734 Optimal Resilient Forwarding Mesh Each source-destination pair is connected by two node-disjoint paths Total number of broadcast transmissions is minimized Minimizing the number of broadcast transmissions is NP-complete Use heuristic algorithms to obtain approximate solutions

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2006/11/0735 Heuristic Approximation Algorithms Tree-based Node-Disjoint Tree Algorithm (NDT) Revised Node-Disjoint Tree Algorithm (RNDT) Path-based Shared Disjoint Mesh Algorithm (SDM) Minimal Disjoint Mesh Algorithm (MDM)

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2006/11/0736 Node-Disjoint Tree Algorithm (NDT) Build a multicast tree PT with minimal number of transmissions using the MNT Remove all intermediate nodes of PT from node set V Find a new minimal multicast tree BT in the new V Add all intermediate nodes of PT and BT to RFM

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2006/11/0737 NDT Example S M1M2 M3 R1R2 S M1 M3 R1R2 S M2 M3 R1R2

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2006/11/0738 NDT Example S M1M2 M3 R1 S M1 M3 R1R2 S M2 M3 R2

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2006/11/0739 Shared Disjoint Mesh Algorithm Find a shortest path P Remove all intermediate nodes of P from V, and find another shortest path B which is node-disjoint to P Update out-flow links of all intermediate nodes to zero Add all intermediate nodes of PT and BT to RFM Repeat above steps for all receivers

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2006/11/0740 SDM Example S M1M2 M3 R1R M2’

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2006/11/0741 Minimal Disjoint Mesh Algorithm Improves SDM in the way of building the node-disjoint path pair Use Suurballe’s algorithm to find node- disjoint path pair with minimal cost at the same time

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2006/11/0742 Suurballe ’ s Algorithm Example S M1M3M2 R S M1M3M2 R Cost = Cost =

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2006/11/0743 Comparison of the 4 Protocols Simulated in QualNet Manually calculate optimal solution up to session size of 10 Performance is measured by the number of transmissions as a function of multicast session size

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2006/11/0744 Performance Comparison NDT RNDT SDM MDM Multicast Session Size Number of Transmissions

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2006/11/0745 Summary NDT and RNDT are tree-based heuristic algorithms SDM and MDM are mesh-based heuristic algorithms MDM used Suurballe’s algorithm to find node-disjoint path pair with minimal cost Total Number of transmissions: MDM

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2006/11/0746 Compare MNT with MDM

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2006/11/0747 Compare MNT with MDM cont. MDM needs additional transmissions to provide resilience MDM needs more transmissions when session size is small When session size increases, the MDM is more likely to find the disjoint paths that share more common intermediate nodes

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2006/11/0748 Outline Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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2006/11/0749 Lecture Summary Ruiz’s The MNT is NP-complete Heuristic Algorithm Centralized Algorithm Distributed Algorithm Chou’s Tree-based: NDT and RNDT Path-based: SDM and MDM Total number of transmissions: MDM

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2006/11/0750 References Heuristic algorithms for minimum bandwidth consumption multicast routing in wireless mesh networks, P. M. Ruiz, and A. F. Gomez-Skarmeta, Proceedings of ADHOC-NOW, Protecting Multicast Sessions in Wireless Mesh Networks, X. Zhou, J. Guo, C.T. Chou, and S. Jha, IEEE Conference on Local Computer Networks, Simulation Study of Diverse Routing and Protection Algorithm in Mesh WDM Network, X. Yao, and C. Chen, A Performance Comparison Study of Ad Hoc Wireless Multicast Protocols, S.J. Lee, W. Su, J. Hsu, M. Gerla, and R. Bagrodia, Proceedings of IEEE INFOCOM, A Fast Algorithm for Steiner Trees, L. Kou, G. Markowsky, and L. Berman, Acta Informatica, No. 15, vol. 2, 1981, pp

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