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Mathematical Programming

, Volume 59, Issue 1–3, pp 413–420 | Cite as

A note on the prize collecting traveling salesman problem

  • Daniel Bienstock
  • Michel X. Goemans
  • David Simchi-Levi
  • David Williamson
Article

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.

Key words

Linear programming prize collecting rounding fractional solutions traveling salesman problem worst-case analysis 

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Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Daniel Bienstock
    • 1
  • Michel X. Goemans
    • 2
  • David Simchi-Levi
    • 3
  • David Williamson
    • 4
  1. 1.Department of Industrial Engineering and Operations ResearchColumbia University in the City of New YorkNew YorkUSA
  2. 2.Department of MathematicsMITCambridgeUSA
  3. 3.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  4. 4.Laboratory for Computer ScienceMITCambridgeUSA

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