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 $$Owh^{2w}n$$Owh2wn on an input graph having n vertices and whose treewidth is bounded by a fixed constant w.