Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Edge-Splitting Problems with Demands
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Augmenting Edge and Vertex Connectivities Simultaneously
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Polyhedral Structure of Submodular and Posi-modular Systems
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
K-Edge and 3-Vertex Connectivity Augmentation in an Arbitrary Multigraph
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Optimal Bi-Level Augmentation for Selectivity Enhancing Graph Connectivity with Applications
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
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Given two undirected multigraphs G = (V, E) and H = (V, K), and two nonnegative integers l and k, we consider the problem of augmenting G and H by a smallest edge set F to obtain an l-edge-connected multigraph G + F = (V, E ∪ F) and a k-vertex-connected multigraph H + F = (V, K ∪ F). The problem includes several augmentation problems that require to increase the edge- and vertex-connectivities simultaneously. In this paper, we show that the problem with l ≥ 2 and k = 2 can be solved by adding at most one edge over the optimum in O(n4) time for two arbitrary multigraphs G and H, where n = |V|. In particular, we show that if l is even, then the problem can be solved optimally.