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Approximation Algorithms for the Traveling Repairman and Speeding Deliveryman Problems

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Abstract

Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a path that visits the maximum possible number of locations during their time windows. In the second variation, the speeding deliveryman problem, the goal is to find a path that uses the minimum possible speedup to visit all locations during their time windows. For both variations, the time windows are of unit length, and the distance metric is based on a weighted, undirected graph. Algorithms with improved approximation ratios are given for the case when the input is defined on a tree rather than a general graph. The algorithms are also extended to handle time windows whose lengths fall in any bounded range.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, 305 N. University Street, West Lafayette, IN, 47907, USA

    Greg N. Frederickson

  2. Department of Computer Science, Elizabethtown College, One Alpha Drive, Elizabethtown, PA, 17022, USA

    Barry Wittman

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  1. Greg N. Frederickson
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  2. Barry Wittman
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Correspondence to Barry Wittman.

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Frederickson, G.N., Wittman, B. Approximation Algorithms for the Traveling Repairman and Speeding Deliveryman Problems. Algorithmica 62, 1198–1221 (2012). https://doi.org/10.1007/s00453-011-9515-4

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  • DOI: https://doi.org/10.1007/s00453-011-9515-4

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