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Approximation Algorithms for the A Priori TravelingRepairman
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 with a root
, the traveling repairman problem (TRP) involves finding a tour
originating from 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 originating from
and visiting all vertices. The objective is to minimize the expected sum of
arrival-times at all active vertices, when 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