COSC 5341 High-Performance Computer Networks Presentation for By Linghai Zhang ID:

Sanjiv Kapoor, Srivatsan Raghavan Global Telecommunications conference, 2000, GLOBECOM’00 Improved Multicast Routing with Delay and Delay Variation Constrains

Outline  Graph Model  Problem description  Proposed algorithm  Analysis of the algorithm  Performance evaluation  Conclusion

Graph Model Directed Graph G(V,E)  V: the entire set of nodes in the multicast.  E: the set of edges in the graph.  Delay Function D and Cost Function C: E -> R+  Source Node: s  Destination Node Set:

Example of the graph V={s,a,b,c,d,e,f} E={(s,a),(s,b),(c,a),(b,c),(b,f),(c,d),(c,e)} S={a,c,d,f} The red number stands for the delay of the edge and the green number represents the cost.

Problem Description Given a delay bound Δ, a variation bound δ, find a multicast tree T such that: and Then try to minimize the total cost

Example of a Multicast Tree The delay of longest path is equal to 10 and the delay variation between different destinations is less than 9 while the total cost of the tree is 14.

The proposed algorithm 1 Find a multicast tree satisfied above requirement is proved to be a NP-Complete problem. The proposed algorithm is a heuristic algorithm. Let the minimum cost path from s to j with delay exactly equal to t. The following recurrence is used.

The proposed algorithm 1(Cont ’ d)

Analysis of the algorithm 1 The algorithm correctly generates minimum cost paths to the multicast nodes if they exist within the delay bound Δand variation bound δ. The overall time complexity is And examples show that the algorithm can finds paths with variation bounds which are not found by DVMA (Delay Variation Bounded Multicast Algorithm) as well as cases where the overall cost of the paths is less than that found by DVMA.

The proposed algorithm 2

Analysis of the algorithm 2

Approximation schemes

Approximation Schemes (Cont ’ d)

Performance Evaluation The figure show that we can find paths with variances an order of magnitude lower than that founded by DVMA

Performance Evaluation (Cont ’ d) The execution times of both the approaches were also much less as compared to that of the DVMA algorithm.

Performance Evaluation (Cont ’ d) DPDVB gives competitive results in terms of the cost of the paths compared to DVMA whereas DPDVBC expectedly does much better.

Performance Evaluation (Cont ’ d)

Conclusion This paper focused on the problem of Multicast Routing with delay boundedness and delay variation boundedness as constraints. A routing protocol is proposed and compared with previous schemes DVMA. The results show that the scheme proposed improves over the DVMA in the variation bounds achieved and is comparatively far more efficient.

any QUESTIONS?  Thanks