2026-07-26T16:59:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12428 2024-03-06T10:50:06Z ddc:004 open_access

Counting Homomorphisms in Plain Exponential Time Bulatov, Andrei A. Dadsetan, Amineh graph homomorphisms plain exponential time clique width 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrei A. Bulatov and Amineh Dadsetan 2020 Is Part Of LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2020.21 urn:nbn:de:0030-drops-124287 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.21 eng https://creativecommons.org/licenses/by/3.0/legalcode