Papers › Linear Search with Probabilistic Detection and Variable Speeds
Linear Search with Probabilistic Detection and Variable Speeds
Jared Coleman, Oscar Morales-Ponce
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We present results on new variants of the famous linear search (or cow-path) problem that involves an agent searching for a target with unknown position on the infinite line. We consider the variant where the agent can move either at speed $1$ or at a slower speed v ∈[0, 1). When traveling at the slower speed v, the agent is guaranteed to detect the target upon passing through its location. When traveling at speed $1$, however, the agent, upon passing through the target's location, detects it with probability p ∈[0, 1]. We present algorithms and provide upper bounds for the competitive ratios for three cases separately: when p=0, v=0, and when p,v ∈(0,1). We also prove that the provided algorithm for the p=0 case is optimal.
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