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.ITCS.2017.14
URN: urn:nbn:de:0030-drops-81775
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8177/
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F├╝rer, Martin

Multi-Clique-Width

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LIPIcs-ITCS-2017-14.pdf (0.4 MB)


Abstract

Multi-clique-width is obtained by a simple modification in the definition of clique-width. It has the advantage of providing a natural extension of tree-width. Unlike clique-width, it does not explode exponentially compared to tree-width. Efficient algorithms based on multi-clique-width are still possible for interesting tasks like computing the independent set polynomial or testing c-colorability. In particular, c-colorability can be tested in time linear in n and singly exponential in c and the width k of a given multi-k-expression. For these tasks, the running time as a function of the multi-clique-width is the same as the running time of the fastest known algorithm as a function of the clique-width. This results in an exponential speed-up for some graphs, if the corresponding graph generating expressions are given. The reason is that the multi-clique-width is never bigger, but is exponentially smaller than the clique-width for many graphs. This gap shows up when the tree-width is basically equal to the multi-clique width as well as when the tree-width is not bounded by any function of the clique-width.

BibTeX - Entry

@InProceedings{frer:LIPIcs:2017:8177,
  author =	{Martin F{\"u}rer},
  title =	{{Multi-Clique-Width}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{14:1--14:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8177},
  URN =		{urn:nbn:de:0030-drops-81775},
  doi =		{10.4230/LIPIcs.ITCS.2017.14},
  annote =	{Keywords: clique-width, parameterized complexity, tree-width, independent set polynomial, graph coloring}
}

Keywords: clique-width, parameterized complexity, tree-width, independent set polynomial, graph coloring
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017


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