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Abstract

Given an arc-weighted directed graph G = (V,A,ℓ) and a pair of vertices s,t, we seek to find an s-twalk of minimum length that visits all the vertices in V. If ℓ satisfies the asymmetric triangle inequality, the problem is equivalent to that of finding an s-tpath of minimum length that visits all the vertices. We refer to this problem as ATSPP. When s = t this is the well known asymmetric traveling salesman tour problem (ATSP). Although an O(logn) approximation ratio has long been known for ATSP, the best known ratio for ATSPP is \(O(\sqrt{n})\). In this paper we present a polynomial time algorithm for ATSPP that has approximation ratio of O(logn). The algorithm generalizes to the problem of finding a minimum length path or cycle that is required to visit a subset of vertices in a given order.

Keywords

Approximation Ratio Travel Salesman Problem Travel Salesman Problem Polynomial Time Algorithm Hamiltonian Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Chandra Chekuri
    • 1
  • Martin Pál
    • 2
  1. 1.Lucent Bell LabsMurray HillUSA
  2. 2.Google Inc.New YorkUSA

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