Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth

Citation

Enright J & Meeks K (2015) Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth. In: Lu Z, Kim D, Wu W, Li W & Du D-Z D (eds.) Combinatorial Optimization and Applications: 9th International Conference, COCOA 2015, Houston, TX, USA, December 18-20, 2015, Proceedings. Lecture Notes in Computer Science, 0302-9743. Combinatorial Optimization and Applications - 9th International Conference, Houston, Texas, 18.12.2015-20.12.2015. Cham, Switzerland: Springer, pp. 574-585. https://doi.org/10.1007/978-3-319-26626-8_42

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.

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