The parameterised complexity of counting connected subgraphs and graph motifs

Jerrum, M. and Meeks, K. (2015) The parameterised complexity of counting connected subgraphs and graph motifs. Journal of Computer and System Sciences, 81(4), pp. 702-716. (doi:10.1016/j.jcss.2014.11.015)

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Abstract

We introduce a family of parameterised counting problems on graphs, p-#Induced Subgraph With Property(Φ), which generalises a number of problems which have previously been studied. This paper focuses on the case in which Φ defines a family of graphs whose edge-minimal elements all have bounded treewidth; this includes the special case in which Φ describes the property of being connected. We show that exactly counting the number of connected induced k-vertex subgraphs in an n-vertex graph is #W[1]-hard, but on the other hand there exists an FPTRAS for the problem; more generally, we show that there exists an FPTRAS for p-#Induced Subgraph With Property(Φ) whenever Φ is monotone and all the minimal graphs satisfying Φ have bounded treewidth. We then apply these results to a counting version of the Graph Motif problem.

Item Type:Articles
Additional Information:NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computer and System Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computer and System Sciences, volume 81, issue 4, 06/2015, http://dx.doi.org/10.1016/j.jcss.2014.11.015
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:Journal of Computer and System Sciences
Journal Abbr.:JCSS
Publisher:Elsevier
ISSN:0022-0000
ISSN (Online):1090-2724
Copyright Holders:Copyright © 2014 Elsevier Inc.
First Published:First published in Journal of Computer and System Sciences 81(4):702-716
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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