## Abstract

The minimum latency problem, also known as the traveling repairman problem, is a variant of the traveling salesman problem in which the starting node of the tour is given and the goal is to minimize the sum of the arrival times at the other nodes. We present a quasi-polynomial time approximation scheme (QPTAS) for this problem when the instance is a weighted tree, when the nodes lie in ℝ^{d} for some fixed d, and for planar graphs. We also present a polynomial time constant factor approximation algorithm for the general metric case. The currently best polynomial time approximation algorithm for general metrics, due to Goemans and Kleinberg, computes a 3.59-approximation.

Original language | English (US) |
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Pages (from-to) | 1317-1337 |

Number of pages | 21 |

Journal | SIAM Journal on Computing |

Volume | 32 |

Issue number | 5 |

DOIs | |

State | Published - Aug 2003 |

## All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)

## Keywords

- Approximation algorithms
- Minimum latency tour
- Quasi-polynomial approximation schemes
- Randomized search ratio
- Search ratio
- Traveling repairman
- Vehicle routing