Approximation Algorithms For The A Priori Traveling Repairman

We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem. Given a metric (V, d) with a root r is an element of 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 tau originating from r and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when tau is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under independent non-uniform probabilities. Our result provides a general reduction from non-uniform to uniform probabilities, and uses (in black-box manner) an existing approximation algorithm for a priori TRP under uniform probabilities. (C) 2020 Elsevier B.V. All rights reserved.