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

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 maximum component size in the resulting graph is at most h. While this problem is NP-complete in general, 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 problem in time O((wh)2wn) on an input graph having n vertices and whose treewidth is bounded by a fixed constant w.