The minimum latency problem

We are given a set of points p1, . . . , pn and a symmetric distance matrix (dij) giving the distance between pi and pj . We wish to construct a tour that minimizes ∑n i=1 `(i), where `(i) is the latency of pi, defined to be the distance 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 diskhead 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. ∗School of Computer Science, CMU. Supported in part by NSF National Young Investigator grant CCR9357793. †School of Computer Science, CMU. ‡IBM T.J. Watson Research Center.