License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.66
URN: urn:nbn:de:0030-drops-164076
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16407/
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Ganian, Robert ; Hamm, Thekla ; Korchemna, Viktoriia ; Okrasa, Karolina ; Simonov, Kirill

The Fine-Grained Complexity of Graph Homomorphism Parameterized by Clique-Width

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Abstract

The generic homomorphism problem, which asks whether an input graph G admits a homomorphism into a fixed target graph H, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of the running time of the homomorphism problem with respect to the clique-width of G (denoted cw) for virtually all choices of H under the Strong Exponential Time Hypothesis. In particular, we identify a property of H called the signature number s(H) and show that for each H, the homomorphism problem can be solved in time O^*(s(H)^cw). Crucially, we then show that this algorithm can be used to obtain essentially tight upper bounds. Specifically, we provide a reduction that yields matching lower bounds for each H that is either a projective core or a graph admitting a factorization with additional properties - allowing us to cover all possible target graphs under long-standing conjectures.

BibTeX - Entry

@InProceedings{ganian_et_al:LIPIcs.ICALP.2022.66,
  author =	{Ganian, Robert and Hamm, Thekla and Korchemna, Viktoriia and Okrasa, Karolina and Simonov, Kirill},
  title =	{{The Fine-Grained Complexity of Graph Homomorphism Parameterized by Clique-Width}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{66:1--66:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16407},
  URN =		{urn:nbn:de:0030-drops-164076},
  doi =		{10.4230/LIPIcs.ICALP.2022.66},
  annote =	{Keywords: homomorphism, clique-width, fine-grained complexity}
}

Keywords: homomorphism, clique-width, fine-grained complexity
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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