Finding Hidden Independent Sets in Interval Graphs

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We design efficient competitive algorithms for discovering information hidden by an adversary. Specifically, consider a game in a given interval grpah G in which the adversary chooses an independent set X in G. Our ogal is to discover this hidden independent set X by making the fewest queries of the form "Is point p covered by an interval in X?" Our interest in this problem stems from two applications: experimental gene discovery with PCR tehcnology and the game of Battleship (in a 1-dimensional setting). We prove adaptive algorithms for both the verification scenario (given an independent set, is it X?) and the discovery scenario (find X without any information). Under some assumptions, these algorithms use an asymptotically optimal number of queries in every instance.

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