Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Finding $k$ Cuts within Twice the Optimal
SIAM Journal on Computing
Randomized rounding without solving the linear program
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SIAM Journal on Computing
Expander flows, geometric embeddings and graph partitioning
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SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Detecting critical nodes in sparse graphs
Computers and Operations Research
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
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Existence Theorems and Approximation Algorithms for Generalized Network Security Games
ICDCS '10 Proceedings of the 2010 IEEE 30th International Conference on Distributed Computing Systems
Complexity of the critical node problem over trees
Computers and Operations Research
The complexity and approximability of minimum contamination problems
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Networks of the Brain
Cut problems in graphs with a budget constraint
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Computers and Operations Research
Branch and cut algorithms for detecting critical nodes in undirected graphs
Computational Optimization and Applications
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In this paper we propose an efficient approximation algorithm for determining solutions to the critical node detection problem (CNDP) on unweighted and undirected graphs. Given a user-defined number of vertices k0, the problem is to determine which k nodes to remove such as to minimize pairwise connectivity in the induced subgraph. We present a simple, yet powerful, algorithm that is derived from a randomized rounding of the relaxed linear programming solution to the CNDP. We prove that the expected solution quality obtained by the linear-time algorithm is bounded by a constant. To highlight the algorithm quality four common complex network models are utilized, in addition to four real-world networks.