A tournament is a digraph in which every pair of vertices is connected by exactly one arc. The score list of a tournament is the sorted list of the out-degrees of its vertices. Given a non-decreasing sequence of non-negative integers, is it the score list of some tournament? There is a simple test for answering this question. There is also a simple sequential algorithm for constructing a tournament with a given score list. However, this algorithm has a greedy nature, and seems hard to parallelize. We present a simple parallel algorithm for the construction problems. Our algorithm runs in time O(logn) and uses O(n^2/logn) processors on a CREW PRAM, where n is the number of vertices. Since the size of the output is Omega(n^2), our algorithm achieves optimal speedup.
Optimal Parallel Construction of Prescribed Tournaments
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