The minimum latency problem

Abstract

We are given a set of points pl, . . . ,p. and a symmetric distance matrix (o!ij ) giving the distance between pi and pj. We wish to construct a tour that minimizes Σn=1 ℓ (i), where l(i) is the latency of p;, defined to be the dist ante traveled before first visiting pi. This problem is also known in the literature as the deliveryman problem or the traveling repairman problem. It arises in a number of applications including disk-head scheduling, and turns out to be surprisingly different from the traveling salesman problem in character. We give exact and approximate solutions to a number of cases, including a constant-factor approximation algorithm whenever the distance matrix satisfies the triangle inequality.