The challenges of unbounded treewidth in parameterised subgraph counting problems

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised problems which involve finding or counting subgraphs with p...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 198; pp. 170 - 194
Main Author: Meeks, Kitty
Format: Journal Article
Language:English
Published: Elsevier B.V 10.01.2016
Subjects:
Counting complexity
FPTRAS
Parameterised complexity
Subgraph counting
Counting complexity
Subgraph counting
FPTRAS
Parameterised complexity
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised problems which involve finding or counting subgraphs with particular properties rely on bounding the treewidth of these subgraphs in some sense; here, we prove a number of hardness results for the situation in which this bounded treewidth condition does not hold, resulting in dichotomies for some special cases of the general subgraph counting problem. The paper also gives a thorough survey of known results on this subject and the methods used, as well as discussing the relationships both between multicolour and uncoloured versions of subgraph counting problems, and between exact counting, approximate counting and the corresponding decision problems.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2015.06.019