The angular-metric traveling salesman problem

Alok Aggarwal, Don Coppersmith, Sanjeev Khanna, Rajeev Motwani, Baruch Schieber

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


Motivated by applications in robotics, we formulate the problem of minimizing the total angle cost of a TSP tour for a set of points in Euclidean space, where the angle cost of a tour is the sum of the direction changes at the points. We establish the NP-hardness of both this problem and its relaxation to the cycle cover problem. We then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of O(log n) in polynomial time. We also consider the problem of simultaneously approximating both the angle and the length measure for a TSP tour. In studying the resulting tradeoff, we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum. Finally, we consider the extremal value of the angle measure and obtain essentially tight bounds for it. In this paper we restrict our attention to the planar setting, but all our results are easily extended to higher dimensions.

Original languageEnglish (US)
Pages (from-to)697-711
Number of pages15
JournalSIAM Journal on Computing
Issue number3
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


  • Angle metric
  • Approximation algorithms
  • Combinatorial optimization
  • Computational complexity
  • Extremal point sets
  • Robotics
  • Traveling salesman problem


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