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Approximating the Bipartite TSP and Its Biased Generalization

  • Aleksandar Shurbevski
  • Hiroshi Nagamochi
  • Yoshiyuki Karuno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)

Abstract

We examine a generalization of the symmetric bipartite traveling salesman problem (TSP) with quadrangle inequality, by extending the cost function of a Hamiltonian tour to include a bias factor β ≥ 1. The bias factor is known and given as a part of the input. We propose a novel heuristic procedure for building Hamiltonian cycles in bipartite graphs, and show that it is an approximation algorithm for the generalized problem with an approximation ratio of \(1+\frac{1+\lambda}{\beta+\lambda}\), where λ is a real parameter dependent on the problem instance. This expression is bounded above by a constant 2, for any positive real λ and β ≥ 1, which improves a previously reported approximation ratio of 16/7. As a part of a composite heuristic, the proposed procedure can contribute to an approximation ratio of \(1+\frac{2}{\zeta+\beta(2-\zeta)}\), where ζ is an approximation ratio for the metric TSP.

Keywords

combinatorial optimization approximation algorithm matroid intersection material handling robot bipartite TSP biased cost 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Aleksandar Shurbevski
    • 1
  • Hiroshi Nagamochi
    • 1
  • Yoshiyuki Karuno
    • 2
  1. 1.Department of Applied Mathematics and PhysicsKyoto UniversitySakyo-kuJapan
  2. 2.Department of Mechanical and System EngineeringKyoto Institute of TechnologySakyo-kuJapan

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