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.ICALP.2020.21
URN: urn:nbn:de:0030-drops-124287
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Bulatov, Andrei A. ; Dadsetan, Amineh

Counting Homomorphisms in Plain Exponential Time

LIPIcs-ICALP-2020-21.pdf (0.6 MB)


In the counting Graph Homomorphism problem (#GraphHom) the question is: Given graphs G,H, find the number of homomorphisms from G to H. This problem is generally #P-complete, moreover, Cygan et al. proved that unless the Exponential Time Hypothesis fails there is no algorithm that solves this problem in time O(|V(H)|^o(|V(G)|)). This, however, does not rule out the possibility that faster algorithms exist for restricted problems of this kind. Wahlström proved that #GraphHom can be solved in plain exponential time, that is, in time O((2k+1)^(|V(G)|+|V(H)|) poly(|V(H)|,|V(G)|)) provided H has clique width k. We generalize this result to a larger class of graphs, and also identify several other graph classes that admit a plain exponential algorithm for #GraphHom.

BibTeX - Entry

  author =	{Andrei A. Bulatov and Amineh Dadsetan},
  title =	{{Counting Homomorphisms in Plain Exponential Time}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-124287},
  doi =		{10.4230/LIPIcs.ICALP.2020.21},
  annote =	{Keywords: graph homomorphisms, plain exponential time, clique width}

Keywords: graph homomorphisms, plain exponential time, clique width
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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