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 |
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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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