Deleting edges to restrict the size of an epidemic: a new application for treewidth

Enright, J. and Meeks, K. (2018) Deleting edges to restrict the size of an epidemic: a new application for treewidth. Algorithmica, 80(6), pp. 1857-1889. (doi:10.1007/s00453-017-0311-7)

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Abstract

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph (of small treewidth) so that the resulting graph avoids a set FF of forbidden subgraphs; of particular interest is the problem of determining whether it is possible to delete at most k edges so that the resulting graph has no connected component of more than h vertices, as this bounds the worst-case size of an epidemic. While even this special case of the problem is NP-complete in general (even when h=3h=3 ), we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the general problem in time 2O(|F|wr)n2O(|F|wr)n  on an input graph having n vertices and whose treewidth is bounded by a fixed constant w, if each of the subgraphs we wish to avoid has at most r vertices. For the special case in which we wish only to ensure that no component has more than h vertices, we improve on this to give an algorithm running in time O((wh)2wn)O((wh)2wn) , which we have implemented and tested on real datasets based on cattle movements.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Enright, Dr Jessica and Meeks, Dr Kitty
Authors: Enright, J., and Meeks, K.
College/School:College of Medical Veterinary and Life Sciences > Institute of Biodiversity Animal Health and Comparative Medicine
College of Science and Engineering > School of Computing Science
Journal Name:Algorithmica
Publisher:Springer
ISSN:0178-4617
ISSN (Online):1432-0541
Published Online:20 April 2017
Copyright Holders:Copyright © 2017 Springer Science+Business Media
First Published:First published in Algorithmica 2017
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
678901EPSRC DTG 2014Mary Beth KneafseyEngineering and Physical Sciences Research Council (EPSRC)EP/M506539/1RSI - RESEARCH STRATEGY & INNOVATION