Therese Biedl, Brona Brejova, Erik D. Demaine, Angele M. Hamel, Alejandro Lopez-Ortiz, Tomas Vinar. Finding Hidden Independent Sets in Interval Graphs. Theoretical Computer Science, 310(1-3):287-307. January 2004. Early version appeared in COCOON 2003.
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We design efficient competitive algorithms for discovering hidden information using few queries. Specifically, consider a game in a given set of intervals (and their implied interval graph G) in which our goal is to discover an (unknown) 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 technology and the game of Battleship (in a 1-dimensional setting). We provide 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.