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: | Meeks, Dr Kitty and Enright, Dr Jessica |
| Authors: | Enright, J., and Meeks, K. |
| College/School: | College of Science and Engineering > School of Computing Science College of Medical Veterinary and Life Sciences > School of Biodiversity, One Health & Veterinary Medicine |
| 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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