Multicast in Wireless Mesh Network
Xuan (William) Zhang
Xun Shi
2006/11/07 2
Outline
Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion
2006/11/07 3
Outline
Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion
2006/11/07 4
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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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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Wireless Mesh Networks
Mesh routers are generally stationary Multi-hop forwarding High speed Reliable power supply
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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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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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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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Drawbacks of MANET multicast in WMNs Complexity of computation
High mobility High Power consumption
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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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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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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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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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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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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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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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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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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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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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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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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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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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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, R6M2
S, R5, R6, M2
M3
S
R1
R2
R3
R4R5 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
R4R5 M2M1
M3
R6
S
R1
R2
R3
R4R5 M2M1
M3
R6
Stop!! All nodes in V now only cover at most 1 receiver
S
R1
R2
R3
R4R5 M2M1
M3
R6
MST heuristics to build Steiner tree
S
R1
R2
R3
R4R5 M2M1
M3
R6
minimal data overhead tree!Hehe!!
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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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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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Performance Evaluation cont. Mean path length (Mean number of hops)
The number of multicast hopsfrom a receiver to the source averaged over the totalnumber of receivers.
MNT, MNT2MSTSPT
Aim at minimize the length of the tree.
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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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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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Outline
Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion
2006/11/07 31
Resilient Forwarding Mesh
Makes multicast robust to node or link failure 2 paths Increases PDR and throughput
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Resilient Forwarding Mesh Example
(a) Network topology (b) Optimal solution (c) Suboptimal solution
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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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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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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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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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NDT ExampleS
M1 M2
M3
R1 R2
S
M1
M3
R1 R2
S
M2
M3
R1 R2
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NDT ExampleS
M1 M2
M3
R1
S
M1
M3
R1 R2
S
M2
M3
R2 R2
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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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SDM ExampleS
M1 M2
M3
R1 R2
2 2
2 2
2 2
2 2
5
5
M2’
1
1
0 0
0 0
0 0
0 0
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Minimal Disjoint Mesh Algorithm Improves SDM in the way of building the nod
e-disjoint path pair Use Suurballe’s algorithm to find node-disjoin
t path pair with minimal cost at the same time
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Suurballe’s Algorithm Example S
M1 M3M2
R
1 110
10
10 1 100
1
S
M1 M3M2
R
1 110
10
10 1 100
1
Cost = 3 + 101 Cost = 11 + 12
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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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Performance Comparison
NDTRNDTSDMMDM
Multicast Session Size
Nu
mb
er
of
Tra
nsm
issi
ons
2006/11/07 45
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<SDM<RNDT<NDT
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Compare MNT with MDM
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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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Outline
Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion
2006/11/07 49
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<SDM<RNDT<NDT
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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, 2005.
Protecting Multicast Sessions in Wireless Mesh Networks, X. Zhou, J. Guo, C.T. Chou, and S. Jha, IEEE Conference on Local Computer Networks, 2006.
Simulation Study of Diverse Routing and Protection Algorithm in Mesh WDM Network, X. Yao, and C. Chen, 2004.
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, 2000.
A Fast Algorithm for Steiner Trees, L. Kou, G. Markowsky, and L. Berman, Acta Informatica, No. 15, vol. 2, 1981, pp.141-145.
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