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

Jessica Enright, Kitty Meeks

Research output: Contribution to journalArticlepeer-review

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 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),
which we have implemented and tested on real datasets based on cattle movements.
Original languageEnglish
Pages (from-to)1857–1889
Number of pages12
JournalAlgorithmica
Volume80
Issue number6
Early online date20 Apr 2017
DOIs
Publication statusPublished - Jun 2018

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