Fixing a Tournament

13 years 6 months ago

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We consider a very natural problem concerned with game manipulation. Let G be a directed graph where the nodes represent players of a game, and an edge from u to v means that u can beat v in the game. (If an edge (u, v) is not present, one cannot match u and v.) Given G and a "favorite" node A, is it possible to set up the bracket of a balanced single-elimination tournament so that A is guaranteed to win, if matches occur as predicted by G? We show that the problem is NPcomplete for general graphs. For the case when G is a tournament graph we give several interesting conditions on the desired winner A for which there exists a balanced single-elimination tournament which A wins, and it can be found in polynomial time.

Virginia Vassilevska Williams

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