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.2023.68
URN: urn:nbn:de:0030-drops-181200
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18120/
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Goldberg, Leslie Ann ; Roth, Marc

Parameterised and Fine-Grained Subgraph Counting, Modulo 2

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LIPIcs-ICALP-2023-68.pdf (0.8 MB)

Abstract

Given a class of graphs ℋ, the problem ⊕Sub(ℋ) is defined as follows. The input is a graph H ∈ ℋ together with an arbitrary graph G. The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H. The goal of this research is to determine for which classes ℋ the problem ⊕Sub(ℋ) is fixed-parameter tractable (FPT), i.e., solvable in time f(|H|)⋅|G|^O(1).
Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕Sub(ℋ) is FPT if and only if the class of allowed patterns ℋ is matching splittable, which means that for some fixed B, every H ∈ ℋ can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices.
Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes ℋ, and (II) all tree pattern classes, i.e., all classes ℋ such that every H ∈ ℋ is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I).

BibTeX - Entry

@InProceedings{goldberg_et_al:LIPIcs.ICALP.2023.68,
  author =	{Goldberg, Leslie Ann and Roth, Marc},
  title =	{{Parameterised and Fine-Grained Subgraph Counting, Modulo 2}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{68:1--68:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18120},
  URN =		{urn:nbn:de:0030-drops-181200},
  doi =		{10.4230/LIPIcs.ICALP.2023.68},
  annote =	{Keywords: modular counting, parameterised complexity, fine-grained complexity, subgraph counting}
}

Keywords: modular counting, parameterised complexity, fine-grained complexity, subgraph counting
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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