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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth
Author(s): Enright, Jessica
Meeks, Kitty
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Keywords: Edge-deletion
Network epidemiology
Graph contagion
Issue Date: Jun-2018
Citation: Enright J & Meeks K (2018) Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth, Algorithmica, 80 (6), pp. 1857-1889.
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 F 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=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)n on an input graph having n vertices and whose treewidth is bounded by a fixed constantw, 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), which we have implemented and tested on real datasets based on cattle movements.
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Rights: This item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. Publisher policy allows this work to be made available in this repository. Published in Algorithmica, June 2018, Volume 80, Issue 6, pp 1857–1889. The final publication is available at Springer via

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