The firebreak problem

Barnetson, K. D., Burgess, A. C., Enright, J. , Howell, J., Pike, D. A. and Ryan, B. (2020) The firebreak problem. Networks, (doi: 10.1002/net.21975) (Early Online Publication)

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Abstract

Suppose we have a network that is represented by a graph G. Potentially a fire (or other type of contagion) might erupt at some vertex of G. We are able to respond to this outbreak by establishing a firebreak at k other vertices of G, so that the fire cannot pass through these fortified vertices. The question that now arises is which k vertices will result in the greatest number of vertices being saved from the fire, assuming that the fire will spread to every vertex that is not fully behind the k vertices of the firebreak. This is the essence of the Firebreak decision problem, which is the focus of this paper. We establish that the problem is intractable on the class of split graphs as well as on the class of bipartite graphs, but can be solved in linear time when restricted to graphs having constant‐bounded treewidth, or in polynomial time when restricted to intersection graphs. We also consider some closely related problems.

Item Type:Articles
Additional Information:Authors Burgess and Pike acknowledge research grant support from NSERC. Ryan acknowledges support from an NSERC Undergraduate Student Research Award. Jessica Enright was partially supported by the Biotechnology and Biological Sciences Research Council. Grant number BB/R009309/1.
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Enright, Dr Jessica
Authors: Barnetson, K. D., Burgess, A. C., Enright, J., Howell, J., Pike, D. A., and Ryan, B.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Networks
Publisher:Wiley
ISSN:0028-3045
ISSN (Online):1097-0037
Published Online:21 August 2020
Copyright Holders:Copyright © 2020 Wiley Periodicals LLC
First Published:First published in Networks 2020
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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