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Infinite linear programming and online searching with turn cost

Abstract : We consider the problem of searching for a hidden target in an environment that consists of a set of concurrent rays. Every time the searcher turns direction , it incurs a fixed cost. The objective is to derive a search strategy for locating the target as efficiently as possible, and the performance of the strategy is evaluated by means of the well-established competitive ratio. In this paper we revisit an approach due to Demaine et al. [TCS 2006] based on infinite linear-programming formulations of this problem. We first demonstrate that their definition of duality in infinite LPs can lead to erroneous results. We then provide a non-trivial correction which establishes the optimality of a certain round-robin search strategy.
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Submitted on : Thursday, February 2, 2017 - 12:33:44 PM
Last modification on : Saturday, December 4, 2021 - 4:04:14 AM
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Spyros Angelopoulos, Diogo Arsénio, Christoph Dürr. Infinite linear programming and online searching with turn cost. Theoretical Computer Science, 2017, ⟨10.1016/j.tcs.2017.01.013⟩. ⟨hal-01452876⟩



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