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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.284
A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs

Authors: Jeremy A. Karp and R. Ravi

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time 9/7-approximation algorithm for cubic bipartite graphs and a (9/7+1/(21(k-2)))-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are able to do by leveraging the fact that all cycles in bipartite graphs are of even length along with our knowledge of the structure of cubic graphs.
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Jeremy A. Karp and R. Ravi. A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 284-296, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{karp_et_al:LIPIcs.APPROX-RANDOM.2014.284,
  author =	{Karp, Jeremy A. and Ravi, R.},
  title =	{{A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{284--296},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.284},
  URN =		{urn:nbn:de:0030-drops-47034},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.284},
  annote =	{Keywords: Approximation algorithms, traveling salesman problem, Barnette’s conjecture, combinatorial optimization}
}
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