The Effect of Asymmetry on the On-Line Multicast Routing Problem

In this paper, we study the problem of multicast routing on directed graphs. We define the asymmetry of a graph to be the maximum ratio of weights on opposite directed edges between a pair of nodes for all node-pairs. We examine three types of problems according the membership behavior: (i) the static, (ii) the join-only, (iii) the join-leave problems. We study the effect of the asymmetry on the worst case performance of two algorithms: the Greedy and Shortest Paths algorithms. The worst case performance of Shortest Paths is poor, but it is affected by neither the asymmetry nor the membership behavior. In contrast, the worst case performance of Greedy is a proportional to the asymmetry in a some cases. We prove an interesting result for the join-only problem: the Greedy algorithm has near-optimal on-line performance.

[1]  Stefan Voß,et al.  Worst-Case Performance of Some Heuristics for Steiner's Problem in Directed Graphs , 1993, Inf. Process. Lett..

[2]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[3]  Graham Knight,et al.  Comparison of dynamic multicast routing algorithms for wide-area packet switched (asynchronous transfer mode) networks , 1995, Proceedings of INFOCOM'95.

[4]  Chak-Kuen Wong,et al.  A faster approximation algorithm for the Steiner problem in graphs , 1986, Acta Informatica.

[5]  Lusheng Wang,et al.  An approximation scheme for some Steiner tree problems in the plane , 1994, Networks.

[6]  Deborah Estrin,et al.  The PIM architecture for wide-area multicast routing , 1996, TNET.

[7]  Anujan Varma,et al.  ARIES: A Rearrangeable Inexpensive Edge-Based On-Line Steiner Algorithm , 1997, IEEE J. Sel. Areas Commun..

[8]  Bernard M. Waxman,et al.  Performance evaluation of multipoint routing algorithms , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[9]  George Markowsky,et al.  A fast algorithm for Steiner trees , 1981, Acta Informatica.

[10]  Jeffery R. Westbrook,et al.  Greedy Algorithms for the On-Line Steiner Tree and Generalized Steiner Problems , 1993, WADS.

[11]  Makoto Imase,et al.  Dynamic Steiner Tree Problem , 1991, SIAM J. Discret. Math..

[12]  Ján Plesník.  Heuristics for the Steiner Problem in Graphs , 1992, Discret. Appl. Math..

[13]  Pawel Winter,et al.  Steiner problem in networks: A survey , 1987, Networks.

[14]  K. Bharath-Kumar,et al.  Routing to Multiple Destinations in Computer Networks , 1983, IEEE Trans. Commun..

[15]  V. J. Rayward-Smith,et al.  The computation of nearly minimal Steiner trees in graphs , 1983 .

[16]  Tao Jiang,et al.  An approximation scheme for some Steiner tree problems in the plane , 1994, Networks.

[17]  Ian M. Leslie,et al.  How bad is naive multicast routing? , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[18]  Jon Crowcroft,et al.  Core Based Trees (CBT) An Architecture for Scalable Inter-Domain Multicast Routing , 1993, SIGCOMM 1993.

[19]  Sudipto Guha,et al.  Approximation algorithms for directed Steiner problems , 1999, SODA '98.

[20]  BERNARD M. WAXMAN,et al.  Routing of multipoint connections , 1988, IEEE J. Sel. Areas Commun..

[21]  J. J. Garcia-Luna-Aceves,et al.  A Protocol for Scalable Loop-Free Multicast Routing , 1997, IEEE J. Sel. Areas Commun..

[22]  S. E. Dreyfus,et al.  The steiner problem in graphs , 1971, Networks.

[23]  A. Zelikovsky.  Better approximation bounds for the network and Euclidean Steiner tree problems , 1996 .