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A note on the prize collecting traveling salesman problem

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Abstract

We study the version of the prize collecting traveling salesman problem, where the objective is to find a 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. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University in the City of New York, 10027-6699, New York, NY, USA

    Daniel Bienstock

  2. Department of Mathematics, MIT, Cambridge, MA, USA

    Michel X. Goemans

  3. Department of Industrial Engineering and Operations Research, Columbia University, New York, USA

    David Simchi-Levi

  4. Laboratory for Computer Science, MIT, Cambridge, MA, USA

    David Williamson

Authors
  1. Daniel Bienstock
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  2. Michel X. Goemans
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  3. David Simchi-Levi
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  4. David Williamson
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Additional information

Research supported in part by ONR contract N00014-90-J-1649 and NSF contract DDM-8922712.

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Bienstock, D., Goemans, M.X., Simchi-Levi, D. et al. A note on the prize collecting traveling salesman problem. Mathematical Programming 59, 413–420 (1993). https://doi.org/10.1007/BF01581256

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  • DOI: https://doi.org/10.1007/BF01581256

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