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On the minimum latency problem

Avrim Blum·Prasad Chalasani·Don Coppersmith·Bill Pulleyblank·Prabhakar Raghavan·Madhu Sudan
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Abstract

We are given a set of points $p_1,\ldots , p_n$ and a symmetric distance matrix $(d_{ij})$ giving the distance between $p_i$ and $p_j$. We wish to construct a tour that minimizes $\sum_{i=1}^n \ell(i)$, where $\ell(i)$ is the {\em latency} of $p_i$, defined to be the distance traveled before first visiting $p_i$. This problem is also known in the literature as the {\em deliveryman problem} or the {\em 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.

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Avrim Blum, Prasad Chalasani, Don Coppersmith, Bill Pulleyblank, Prabhakar Raghavan, Madhu Sudan. 1994-09-21. On the minimum latency problem. https://arxiv.org/abs/math/9409223

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