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Approximating the asymmetric profitable tour

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  • Viet Hung Nguyen
  • Thi Thu Thuy Nguyen

Abstract

We study the version of the asymmetric prize collecting travelling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. In Dell'Amico et al. (1995), the authors defined it as the Profitable Tour Problem (PTP). We present an (1 + ⌈log(n)⌉)-approximation algorithm for the asymmetric PTP with n is the vertex number. The algorithm that is based on Frieze et al.'s heuristic for the asymmetric travelling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers (feasible solution for the original problem), represents a directed version of the Bienstock et al.'s (1993) algorithm for the symmetric PTP.

Suggested Citation

  • Viet Hung Nguyen & Thi Thu Thuy Nguyen, 2012. "Approximating the asymmetric profitable tour," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(3), pages 294-301.
    • Handle: RePEc:ids:ijmore:v:4:y:2012:i:3:p:294-301
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    Cited by:

    1. Viet Hung Nguyen, 2013. "A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP," Journal of Combinatorial Optimization, Springer, vol. 25(2), pages 265-278, February.

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