License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2015.125
URN: urn:nbn:de:0030-drops-56264
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5626/
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Chiplunkar, Ashish ; Vishwanathan, Sundar

Approximating the Regular Graphic TSP in Near Linear Time

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Abstract

We present a randomized approximation algorithm for computing traveling salesperson tours in undirected regular graphs. Given an n-vertex, k-regular graph, the algorithm computes a tour of length at most (1+frac 4+ln 4+varepsilon ln k-O(1)n, with high probability, in O(nk log k) time. This improves upon the result by Vishnoi ([Vishnoi12],FOCS 2012) for the same problem, in terms of both approximation factor, and running time. Furthermore, our result is incomparable with the recent result by Feige, Ravi, and Singh ([FeigeRS14], IPCO 2014), since our algorithm runs in linear time, for any fixed k. The key ingredient of our algorithm is a technique that uses edge-coloring algorithms to sample a cycle cover with O(n/log k) cycles, with high probability, in near linear time.

Additionally, we also give a deterministic frac{3}{2}+O(frac{1}sqrt{k}) factor approximation algorithm for the TSP on n-vertex, k-regular graphs running in time O(nk).

BibTeX - Entry

@InProceedings{chiplunkar_et_al:LIPIcs:2015:5626,
  author =	{Ashish Chiplunkar and Sundar Vishwanathan},
  title =	{{Approximating the Regular Graphic TSP in Near Linear Time}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{125--135},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Prahladh Harsha and G. Ramalingam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5626},
  URN =		{urn:nbn:de:0030-drops-56264},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.125},
  annote =	{Keywords: traveling salesperson problem, approximation, linear time}
}

Keywords: traveling salesperson problem, approximation, linear time
Collection: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)
Issue Date: 2015
Date of publication: 14.12.2015

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