Discrete & Computational Geometry

, Volume 27, Issue 4, pp 635–651 | Cite as

Approximation Results for Kinetic Variants of TSP

  • Hammar
  • Nilsson
Article

Abstract

We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem (TSP) where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results:

• If the points all move with the same velocity, then there is a polynomial time approximation scheme for the Kinetic TSP.

• The Kinetic TSP cannot be approximated better than by a factor of 2 by a polynomial time algorithm unless P = NP, even if there are only two moving points in the instance.

• The Kinetic TSP cannot be approximated better than by a factor of
$$2^{\Omega(\sqrt{n})}$$
by a polynomial time algorithm unless P = NP, even if the maximum velocity is bounded. n denotes the size of the input instance.

The last result is especially surprising in the light of existing polynomial time approximation schemes for the static version of the problem.

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Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Hammar
    • 1
  • Nilsson
    • 2
  1. 1.Department of Computer Science, Lund University, Box 118, S-221 00 Lund, Sweden mikael@cs.lth.seSweden
  2. 2.School of Technology and Society, Malmö University College, Citadellsvägen 7, 205 06 Malmö, Sweden bengt.nilsson@ts.mah.seSweden

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