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### On the minimum latency problem

**1994-09-21**

9409223 | math.CO

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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