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Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2007, RANDOM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4627))

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Abstract

This paper studies vehicle routing problems on asymmetric metrics. Our starting point is the directed k -TSP problem: given an asymmetric metric (V,d), a root r ∈ V and a target k ≤ |V|, compute the minimum length tour that contains r and at least k other vertices. We present a polynomial time O(log2 n·logk)-approximation algorithm for this problem. We use this algorithm for directed k-TSP to obtain an O(log2 n)-approximation algorithm for the directed orienteering problem. This answers positively, the question of poly-logarithmic approximability of directed orienteering, an open problem from Blum et al.[2]. The previously best known results were quasi-polynomial time algorithms with approximation guarantees of O(log2 k) for directed k-TSP, and O(logn) for directed orienteering (Chekuri & Pal [4]). Using the algorithm for directed orienteering within the framework of Blum et al.[2] and Bansal et al.[1], we also obtain poly-logarithmic approximation algorithms for the directed versions of discounted-reward TSP and the vehicle routing problem with time-windows.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh PA 15213, USA

    Viswanath Nagarajan & R. Ravi

Authors
  1. Viswanath Nagarajan
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  2. R. Ravi
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Editors and Affiliations

  1. Computer Science Dept., Princeton University, 35 Olden Street, NJ 08540-5233, Princeton, USA

    Moses Charikar

  2. Institut für Informatik, Christian-Albrechts-Universität zu Kiel,, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Omer Reingold

  4. Centre Universitaire d’Informatique,, Battelle bâtiment A, route de Drize 7, 1227, Geneva, Carouge, Switzerland

    José D. P. Rolim

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© 2007 Springer-Verlag Berlin Heidelberg

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Nagarajan, V., Ravi, R. (2007). Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_19

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  • DOI: https://doi.org/10.1007/978-3-540-74208-1_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74207-4

  • Online ISBN: 978-3-540-74208-1

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