Abstract
This paper introduces a graph model, conflict graph, to represent the conflict resolution problem in multistage interconnection networks. This model shows that the conflict resolution problem is NP-complete, since it is equivalent to node coloring problem in conflict graph. Three heuristic polynomial algorithms for conflict resolution are presented. The first algorithm with time complexity O(N3) guarantees the performance A(G) = (log N) ** where N is the number of nodes in conflict graph G. This result is a considerable improvement over the best currently known algorithm, which guarantees the performance A(G) ≤ k(G) N1 - 1/k(G) - 1 where k(G) is the chromatic number of graph G. The other two algorithms with time complexity 0(N log N) are more practical, the average number of passes of these algorithms is less than 2 log N - 1 when N is less than given bound.
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