Fast Approximation Algorithms for Finding Node-Independent Paths in Networks

Santa Fe Institute Working Papers Series

9 Pages Posted: 9 May 2011

See all articles by Douglas R. White

Douglas R. White

University of California, Irvine - Department of Anthropology

Mark Newman

University of Michigan at Ann Arbor

Date Written: June 29, 2001

Abstract

A network is robust to the extent that it is not vulnerable to disconnection by removal of nodes. The minimum number of nodes that need be removed to disconnect a pair of other nodes is called the connectivity of the pair. It can be proved that the connectivity is also equal to the number of node-independent paths between nodes, and hence we can quantify network robustness by calculating numbers of node-independent paths. Unfortunately, computing such numbers is known to be an NP-hard problem, taking exponentially long to run to completion. In this paper, we present an approximation algorithm which gives good lower bounds on numbers of node-independent paths between any pair of nodes on a directed or undirected graph in worst-case time which is linear in the graph size. A variant of the same algorithm can also calculate all the k-components of a graph in the same approximation. Our algorithm is found empirically to work with better than 99% accuracy on random graphs and for several real-world networks is 100% accurate. As a demonstration of the algorithm, we apply it to two large graphs for which the traditional NP-hard algorithm is entirely intractable – a network of collaborations between scientists and a network of business ties between biotechnology firms.

Keywords: Networks, Cohesion, Pairwise, Menger Theorem, Algorithm, Graph Theory

Suggested Citation

White, Douglas R. and Newman, Mark, Fast Approximation Algorithms for Finding Node-Independent Paths in Networks (June 29, 2001). Santa Fe Institute Working Papers Series, Available at SSRN: https://ssrn.com/abstract=1831790 or http://dx.doi.org/10.2139/ssrn.1831790

Douglas R. White (Contact Author)

University of California, Irvine - Department of Anthropology ( email )

Irvine, CA 92697¿5100
United States

Mark Newman

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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