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Constant-Factor Approximation for TSP with Disks

In: A Journey Through Discrete Mathematics

Author

Listed:
  • Adrian Dumitrescu

    (University of Wisconsin–Milwaukee, Department of Computer Science)

  • Csaba D. Tóth

    (California State University, Northridge, Department of Mathematics
    Tufts University, Department of Computer Science)

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.

Suggested Citation

  • Adrian Dumitrescu & Csaba D. Tóth, 2017. "Constant-Factor Approximation for TSP with Disks," Springer Books, in: Martin Loebl & Jaroslav Nešetřil & Robin Thomas (ed.), A Journey Through Discrete Mathematics, pages 375-390, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44479-6_15
    DOI: 10.1007/978-3-319-44479-6_15
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