Infinite linear programming and online searching with turn cost

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. [8] 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.