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.2015.246
URN: urn:nbn:de:0030-drops-56493
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5649/
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Balaji, Nikhil ; Datta, Samir ; Ganesan, Venkatesh

Counting Euler Tours in Undirected Bounded Treewidth Graphs

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Abstract

We show that counting Euler tours in undirected bounded tree-width graphs is tractable even in parallel - by proving a GapL upper bound. This is in stark contrast to #P-completeness of the same problem in general graphs.

Our main technical contribution is to show how (an instance of) dynamic programming on bounded clique-width graphs can be performed efficiently in parallel. Thus we show that the sequential result of Espelage, Gurski and Wanke for efficiently computing Hamiltonian paths in bounded clique-width graphs can be adapted in the parallel setting to count the number of Hamiltonian paths which in turn is a tool for counting the number of Euler tours in bounded tree-width graphs. Our technique also yields parallel algorithms for counting longest paths and bipartite perfect matchings in bounded-clique width graphs.

While establishing that counting Euler tours in bounded tree-width graphs can be computed by non-uniform monotone arithmetic circuits of polynomial degree (which characterize #SAC^1) is relatively easy, establishing a uniform #SAC^1 bound needs a careful use of polynomial interpolation.

BibTeX - Entry

@InProceedings{balaji_et_al:LIPIcs:2015:5649,
  author =	{Nikhil Balaji and Samir Datta and Venkatesh Ganesan},
  title =	{{Counting Euler Tours in Undirected Bounded Treewidth Graphs}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{246--260},
  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/2015/5649},
  URN =		{urn:nbn:de:0030-drops-56493},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.246},
  annote =	{Keywords: Euler Tours, Bounded Treewidth, Bounded clique-width, Hamiltonian cycles, Parallel algorithms}
}

Keywords: Euler Tours, Bounded Treewidth, Bounded clique-width, Hamiltonian cycles, Parallel algorithms
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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