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Bounds on the Performance of Message Routing Heuristics
October 1993 (vol. 42 no. 10)
pp. 1253-1256

Let S be a set of messages to be routed on an N*N omega network. In addition, suppose that S contains communication conflicts. One strategy to deal with such conflicts is to partition S into some number of subsets, called rounds, such that each subset is conflict-free. The messages are then routed through the network by successively routing the messages in each subset. The minimum round partitioning problem is the problem of partitioning a given message set into a minimum number of rounds. The author establishes upper and lower bounds on the performance ratio for two heuristics for partitioning message patterns into rounds. For both of these heuristics they give upper and lower bounds of O (log N) and Omega (logN), respectively.

[1] D. P. Agrawal, "Graph theoretical analysis and design of multistage interconnection networks,"IEEE Trans. Comput., vol. C-32, pp. 637-648, July 1983.
[2] P. J. Bernhard, and D. J. Rosenkrantz, "The complexity of routing through an omega network," inProc. Twenty-Fifth Annual Allerton Conf. on Communication, Control and Computing, Sept. 1987, pp. 1027-1036. (Also to appear inIEEE Trans. Parallel Distributed Syst.)
[3] B. Berger, and J. Rompel, "A better performance guarantee for approximate graph coloring,"Algorithmica 5, pp. 459-466, 1990.
[4] P. J. Bernherd and D. J. Rosenkrantz, "An efficient method for representing and transmitting message patterns on multiprocessor interconnection networks,"J. Parallel Distributed Comput., vol. 11, pp. 72-85, 1991.
[5] J. S. Deogun, and Z. Fang, "A heuristic algorithm for conflict resolution problem in multistage interconnection networks, inProc. 1987 Int. Conf. Parallel Processing, pp. 475-478.
[6] D. D. Gajski,et al., "Cedar-A large scale microprocessor,"Proc. 1983 Int. Conf. Parallel Processing, Aug. 1983, pp. 524-529.
[7] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[8] M. M. Halldorsson, "A still better performance guarantee for approximate graph coloring,"DIMACS Tech. Rep. 90-44, Department of Computer Science, Rutgers University, June, 1990.
[9] D. S. Johnson, "Worst case behavior of graph coloring algorithms," inProc. 5th Southeastern Conf. Combinatorics, Graph Theory and Computing, 1974, pp. 513-527.
[10] D. H. Lawrie, "Access and alignment of data in an array processor,"IEEE Trans. Comput., vol. C-21, pp. 1145-1155, Dec. 1975.
[11] C. S. Raghavendra and A. Varma, "Fault-tolerant multiprocessors with redundant path interconnection network,"IEEE Trans. Comput., vol. C-35, no. 4, pp. 307-316, Apr. 1986.
[12] A. Wigderson, "Improving the performance guarantee for approximate graph coloring,"J. ACM, Oct. 1983.
[13] C. L. Wu, and T. Y. Feng, "On a class of multistage interconnection networks,"IEEE Trans. Comput., vol. C-29, pp. 694-702, Aug. 1980.

Index Terms:
performance; message routing heuristics; omega network; communication conflicts; conflict-free; minimum round partitioning problem; heuristics; message patterns; lower bounds; upper bounds; computational complexity; message passing; multiprocessor interconnection networks; network routing; performance evaluation.
P.J. Bernhard, "Bounds on the Performance of Message Routing Heuristics," IEEE Transactions on Computers, vol. 42, no. 10, pp. 1253-1256, Oct. 1993, doi:10.1109/12.257719
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