TSP with neighborhoods of varying size

Mark De Berg, Joachim Gudmundsson, Matthew J. Katz, Christos Levcopoulos, Mark H. Overmars, A. Frank Van Der Stappen

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


In TSP with neighborhoods (TSPN) we are given a collection S of regions in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Until now constant-factor approximation algorithms have been known only for cases where the neighborhoods are of approximately the same size. In this paper we present the first polynomial-time constant-factor approximation algorithm for disjoint convex fat neighborhoods of arbitrary size. We also show that in the general case, where the neighborhoods can overlap and are not required to be convex or fat, TSPN is APX-hard and cannot be approximated within a factor of 391/390 in polynomial time, unless P=NP.

Original languageEnglish
Pages (from-to)22-36
Number of pages15
JournalJournal of Algorithms
Issue number1
StatePublished - 1 Sep 2005


  • Approximation algorithms
  • Computational geometry
  • TSP with neighborhoods

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics


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