Infinite linear programming and online searching with turn cost

Spyros Angelopoulos 1, * Diogo Arsénio 2, * Christoph Dürr 1, *
* Corresponding author
1 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
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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Spyros Angelopoulos, Diogo Arsénio, Christoph Dürr. Infinite linear programming and online searching with turn cost. Theoretical Computer Science, Elsevier, 2017, ⟨10.1016/j.tcs.2017.01.013⟩. ⟨hal-01452876⟩

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