Exact and Approximation Algorithms for the Expanding Search Problem

Suppose a target is hidden in one of the vertices an edge-weighted graph according to known probability distribution. Starting from fixed root node, expanding search visits sequentially until it finds target, where next vertex can be reached any previously visited vertices. That is, time reach equals shortest-path distance set all The problem then asks for sequence nodes, so as minimize expected finding target. This has numerous applications, such searching explosives, mining coal, and disaster relief. In this paper, we develop exact algorithms heuristics, including branch-and-cut procedure, greedy algorithm with constant-factor approximation guarantee, local procedure based on spanning-tree neighborhood. Computational experiments show that our outperforms existing methods instances nonuniform distributions both heuristics compute near-optimal solutions little computational effort. Summary Contribution: paper studies new problem, which nodes applications We propose several algorithms, algorithm, procedure; analyze their performance experimentally theoretically. Our analysis shows improve establishes first guarantee problem.