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• W3138370239 abstract "Abstract We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem in fixed-parameter tractable and $$#mathsf {W[1]}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>#</mml:mo> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo>[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:mrow> </mml:math> -complete cases. The proof relies on the framework of linear combinations of homomorphisms as independently discovered by Chen and Mengel (PODS 16) and by Curticapean, Dell and Marx in the recent breakthrough result regarding the exact complexity of the subgraph counting problem (STOC 17). Moreover, we invoke Rota’s NBC-Theorem to obtain an explicit criterion for fixed-parameter tractability based on treewidth. The abstract classification theorem is then applied to the problem of counting locally injective graph homomorphisms from small pattern graphs to large target graphs. As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs." @default.
• W3138370239 created "2021-03-29" @default.
• W3138370239 creator A5091690351 @default.
• W3138370239 date "2021-03-11" @default.
• W3138370239 modified "2023-09-26" @default.
• W3138370239 title "Parameterized Counting of Partially Injective Homomorphisms" @default.
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• W3138370239 doi "https://doi.org/10.1007/s00453-021-00805-y" @default.
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