Approximation Algorithms for the A Priori TravelingRepairman
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We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem (also called the traveling deliveryman or minimum latency problem). Given a metric (V,d) with a root r∈ V, the traveling repairman problem (TRP) involves finding a tour originating from r that minimizes the sum of arrival-times at all vertices. In its a priori version, we are also given independent probabilities of each vertex being active. We want to find a master tour τ originating from r and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when τ is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under non-uniform probabilities. Previously, such a result was only known for uniform probabilities.
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