Article in Journal
Enright J & Meeks K (2017) Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth (Forthcoming/Available Online), Algorithmica.
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.
Edge-deletion; Treewidth; Network epidemiology; Graph contagion
|Authors||Enright Jessica, Meeks Kitty|
|Publication date online||20/04/2017|
|Date accepted by journal||11/04/2017|