Toward a general theory of unicast-based multicast communication
Multicast, also known as one-to-many communication, is the problem of sending a message from a single source node to several destination nodes. In this paper, we study the problem of implementing multicasts via a technique called Unicast-Based Multicast (UBM). In particular, we focus on the problem of finding optimal UBM calling schedules for arbitrary topologies using restricted inclusive routing schemes (a natural class of restricted routing schemes which includes most practically implemented restricted routing schemes) given source limited routing information. Previous work has focused on finding optimal UBM calling schedules for arbitrary topologies using free routing schemes given complete routing information and specific topologies using specific restricted routing schemes given complete routing information. We first show that implementing UBM in arbitrary topologies with restricted routing schemes is fundamentally different than implementing UBM in arbitrary topologies with free routing schemes. We then develop the Smart Centroid Algorithm, a polynomial time approximation algorithm which produces UBM calling schedules that are at most four times as long as the optimal UBM calling schedule for arbitrary topologies using restricted inclusive routing schemes given source limited routing information. The question of determining the NP-hardness of producing optimal UBM calling schedules for arbitrary topologies using any restricted routing scheme remains open.
Unable to display preview. Download preview PDF.
- 1.L. M. Ni and P. K. McKinley, “A survey of wormhole routing techniques in direct networks,”; IEEE Computer, vol. 26, pp. 62–76, February 1993.Google Scholar
- 2.P. K. McKinley, H. Xu, A-H. Esfahanian, and L. M. Ni, “Unicast-based multicast communication in wormhole-routed networks,”; IEEE Transactions on Parallel and Distributed Systems, vol. 5, pp. 1252–1265, December 1994.Google Scholar
- 3.A. M. Farley, “Minimal broadcast networks,”; Networks, vol. 9, pp. 313–332, 1979.Google Scholar
- 4.A. M. Farley, “Minimum-time line broadcast networks,”; Networks, vol. 10, pp. 59–70, 1980.Google Scholar
- 5.D. F. Robinson, P. K. McKinley, and B. H. C. Cheng, “Optimal multicast communication in wormhole-routed torus networks,”; in 1994 International Conference on Parallel Processing, pp. I-134–I-141, 1994.Google Scholar
- 6.S. Even, Graph Algorithms. Rockville, MD: Computer Science Press, Inc., 1979.Google Scholar
- 7.B. D. Birchler, A-H. Esfahanian, and E. Torng, “Toward a general theory of unicastbased multicast communication,”; Tech. Rep. CPS-95-3, Michigan State University, March 1995.Google Scholar
- 8.F. Harary, Graph Theory. Addison-Wesley Series In Mathematics, Reading, Massachusetts: Addison-Wesley Publishing Company, 1969.Google Scholar