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Fast Approximation Algorithms for Finding Node-Independent Paths in Networks

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  • Douglas R. White
  • M. E. J. Newman

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.

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Bibliographic Info

Paper provided by Santa Fe Institute in its series Working Papers with number 01-07-035.

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Date of creation: Jul 2001
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Handle: RePEc:wop:safiwp:01-07-035

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Keywords: Graph theory; social networks; cohesion; algorithms;

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