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.


Approximation Ratio Travel Salesman Problem Travel Salesman Problem Polynomial Time Algorithm Hamiltonian Cycle 
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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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