Constant-Factor Approximation for TSP with Disks

Chapter

Abstract

We revisit the traveling salesman problem with neighborhoods (TSPN) and present the first constant-ratio approximation for disks in the plane: Given a set of n disks in the plane, a TSP tour whose length is at most O(1) times the optimal can be computed in time that is polynomial in n. Our result is the first constant-ratio approximation for a class of planar convex bodies of arbitrary size and arbitrary intersections.

In order to achieve a O(1)-approximation, we reduce the traveling salesman problem with disks, up to constant factors, to a minimum weight hitting set problem in a geometric hypergraph. The connection between TSPN and hitting sets in geometric hypergraphs, established here, is likely to have future applications.

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Copyright information

© Springer International publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Wisconsin–MilwaukeeMilwaukeeUSA
  2. 2.Department of MathematicsCalifornia State University, NorthridgeLos AngelesUSA
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA

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