Fast Approximation Algorithms for Finding Node-Independent Paths in Networks
AbstractA 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 InfoPaper provided by Santa Fe Institute in its series Working Papers with number 01-07-035.
Date of creation: Jul 2001
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Graph theory; social networks; cohesion; algorithms;
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