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We consider an agent seeking to obtain an item, potentially available atdifferent locations in a physical environment. The traveling costs betweenlocations are known in advance, but there is only probabilistic knowledgeregarding the possible prices of the item at any given location. Given such asetting, the problem is to find a plan that maximizes the probability ofacquiring the good while minimizing both travel and purchase costs. Sampleapplications include agents in search-and-rescue or exploration missions, e.g.,a rover on Mars seeking to mine a specific mineral. These probabilisticphysical search problems have been previously studied, but we present the firstapproximation and heuristic algorithms for solving such problems on generalgraphs. We establish an interesting connection between these problems andclassical graph-search problems, which led us to provide the approximationalgorithms and hardness of approximation results for our settings. We furthersuggest several heuristics for practical use, and demonstrate theireffectiveness with simulation on real graph structure and synthetic graphs.

Approximation and Heuristic Algorithms for Probabilistic Physical Search on General Graphs