The hardness of approximation: gap location
Computational Complexity
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Finding the most prominent group in complex networks
AI Communications - Network Analysis in Natural Sciences and Engineering
Incremental deployment of network monitors based on Group Betweenness Centrality
Information Processing Letters
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
Betweenness estimation in OLSR-based multi-hop networks for distributed filtering
Journal of Computer and System Sciences
| Hi-index | 0.00 |
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.