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Euclidean TSP

  • Vijay V. Vazirani

Abstract

In this chapter, we will give a PTAS for the special case of the traveling salesman problem in which the points are given in a d-dimensional Euclidean space. As before, the central idea of the PTAS is to define a “coarse solution”, depending on the error parameter ε, and to find it using dynamic programming. A feature this time is that we do not know a deterministic way of specifying the coarse solution — it is specified probabilistically.

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Notes

  1. 10.
    S. Arora. Polynomial time approximation scheme for Euclidean TSP and other geometric problems. In Proc. 37th IEEE Annual Symposium on Foundations of Computer Science, pages 2–11, 1996.Google Scholar
  2. 121.
    M. Grigni, E. Koutsoupias, and C. Papadimitriou. An approximation scheme for planar graph TSP. In Proc. 36th IEEE Annual Symposium on Foundations of Computer Science, pages 640–646, 1995.CrossRefGoogle Scholar
  3. 215.
    J.S.B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM Journal on Computing, 28: 1298–1309, 1999.MathSciNetCrossRefGoogle Scholar
  4. 11.
    S. Arora. Nearly linear time approximation scheme for Euclidean TSP and other geometric problems. In Proc. 38th IEEE Annual Symposium on Foundations of Computer Science, pages 554–563, 1997.CrossRefGoogle Scholar
  5. 237.
    S. Rao and W.D. Smith. Approximating geometrical graphs via “spanners” and “banyan”. In Proc. 30th ACM Symposium on the Theory of Computing, pages 540–550, 1998.Google Scholar
  6. 14.
    S. Arora, P. Raghavan, and S. Rao. Approximation schemes for Euclidean k-medians and related problems. In Proc. 30th ACM Symposium on the Theory of Computing, pages 106–113, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vijay V. Vazirani
    • 1
  1. 1.Georgia Institute of TechnologyCollege of ComputingAtlantaUSA

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