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On Approximating the TSP with Intersecting Neighborhoods

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44374

Elbassioni,  Khaled
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44429

Fishkin,  Aleksei V.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45495

Sitters,  Rene
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44035

Asano,  Tetsuo
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Elbassioni, K., Fishkin, A. V., & Sitters, R. (2006). On Approximating the TSP with Intersecting Neighborhoods. In Algorithms and Computation: 17th International Symposium, ISAAC 2006 (pp. 213-222). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2391-E
Abstract
In the TSP with neighborhoods problem we are given a set of $n$ regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give two approximation algorithms for the case when the regions are allowed to intersect: We give the first $O(1)$-factor approximation algorithm for intersecting convex fat objects of comparable diameters where we are allowed to hit each object only at a finite set of specified points. The proof follows from two packing lemmas that are of independent interest. For the problem in its most general form (but without the specified points restriction) we give a simple $O(\log n)$-approximation algorithm.