The (sigma+1)-Edge-Connectivity Augmentation Problem without Creating Multiple Edges of a Graph
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Graph connectivity and its augmentation: applications of MA orderings
Discrete Applied Mathematics
Edge-splittings preserving local edge-connectivity of graphs
Discrete Applied Mathematics
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Efficient edge splitting-off algorithms maintaining all-pairs edge-connectivities
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks
Journal of Combinatorial Optimization
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Given a simple graph G=(V,E), our goal is to find a smallest set F of new edges such that G=(V,E\cup F) is k-edge-connected and simple. Recently this problem was shown to be NP-complete. In this paper we prove that if OPT_P^k$ is high enough---depending on k only---then OPT _S^k= OPT_P^k$ holds, where OPT_S^k$ (OPT_P^k$) is the size of an optimal solution of the augmentation problem with (without) the simplicity-preserving requirement, respectively. Furthermore, OPT_S^k- OPT _P^k\leq g(k) holds for a certain (quadratic) function of k. Based on these facts an algorithm is given which computes an optimal solution in time O(n4) for any fixed k. Some of these results are extended to the case of nonuniform demands as well.