Abstract
The Maximum Betweenness Centrality problem (MBC) can be defined as follows. Given a graph find a k-element node set C that maximizes the probability of detecting communication between a pair of nodes s and t chosen uniformly at random. It is assumed that the communication between s and t is realized along a shortest s–t path which is, again, selected uniformly at random. The communication is detected if the communication path contains a node of C.
Recently, Dolev et al. (2009) showed that MBC is NP-hard and gave a (1 − 1/e)-approximation using a greedy approach. We provide a reduction of MBC to Maximum Coverage that simplifies the analysis of the algorithm of Dolev et al. considerably. Our reduction allows us to obtain a new algorithm with the same approximation ratio for a (generalized) budgeted version of MBC. We provide tight examples showing that the analyses of both algorithms are best possible. Moreover, we prove that MBC is APX-complete and provide an exact polynomial-time algorithm for MBC on tree graphs.
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Fink, M., Spoerhase, J. (2011). Maximum Betweenness Centrality: Approximability and Tractable Cases. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_4
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DOI: https://doi.org/10.1007/978-3-642-19094-0_4
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