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arXiv · 1504.05773

Deleting edges to restrict the size of an epidemic

Jessica Enright·Kitty Meeks
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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 $\mathcal{F}$ 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 \genruntime ~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 $O((wh)^{2w}n)$, which we have implemented and tested on real datasets based on cattle movements.

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Jessica Enright, Kitty Meeks. 2015-04-22. Deleting edges to restrict the size of an epidemic. https://arxiv.org/abs/1504.05773

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