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Polynomially solvable cases of the bipartite traveling salesman problem

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  • García, Alfredo
  • Tejel, Javier

Abstract

Given two sets, R and B, consisting of n cities each, in the bipartite traveling salesman problem one looks for the shortest way of visiting alternately the cities of R and B, returning to the city of origin. This problem is known to be NP-hard for arbitrary sets R and B. In this paper we provide an O(n6) algorithm to solve the bipartite traveling salesman problem if the quadrangle property holds. In particular, this algorithm can be applied to solve in O(n6) time the bipartite traveling salesman problem in the following cases: S=R∪B is a convex point set in the plane, S=R∪B is the set of vertices of a simple polygon and V=R∪B is the set of vertices of a circular graph. For this last case, we also describe another algorithm which runs in O(n2) time.

Suggested Citation

  • García, Alfredo & Tejel, Javier, 2017. "Polynomially solvable cases of the bipartite traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 429-438.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:2:p:429-438
    DOI: 10.1016/j.ejor.2016.07.060
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    References listed on IDEAS

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    1. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    2. Anand Srivastav & Hartmut Schroeter & Christoph Michel, 2001. "Approximation Algorithms for Pick-and-Place Robots," Annals of Operations Research, Springer, vol. 107(1), pages 321-338, October.
    3. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
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