Some hard families of parameterised counting problems

Jerrum, M. and Meeks, K. (2015) Some hard families of parameterised counting problems. ACM Transactions on Computation Theory, 7(3), 11. (doi:10.1145/2786017)

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Abstract

We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices induce a subgraph with a given property? A number of such problems are known to be #W[1]-complete; here we substantially generalise some of these existing results by proving hardness for two large families of such problems. We demonstrate that it is #W[1]-hard to count the number of k-vertex subgraphs having any property where the number of distinct edge-densities of labelled subgraphs that satisfy the property is o(k^2). In the special case that the property in question depends only on the number of edges in the subgraph, we give a strengthening of this result which leads to our second family of hard problems.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty
Authors: Jerrum, M., and Meeks, K.
Subjects:Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:ACM Transactions on Computation Theory
Publisher:ACM
ISSN:1942-3454
ISSN (Online):1942-3462
Copyright Holders:Copyright © 2015 ACM
First Published:First published in ACM Transactions on Computation Theory 7(3):11
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.
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