Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Efficient splitting off algorithms for graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Graph connectivity and its augmentation: applications of MA orderings
Discrete Applied Mathematics
Approximating connectivity augmentation problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Note: Covering symmetric semi-monotone functions
Discrete Applied Mathematics
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For a finite ground set V, we call a set-function r : 2V → Z+ monotone, if r(X') ≥ r(X) holds for each X'⊆ X ⊆ V, where Z+ is the set of nonnegative integers. Given an undirected multigraph G = (V, E) and a monotone requirement function r: 2V → Z+, we consider the problem of augmenting G by a smallest number of new edges so that the resulting graph G' satisfies dG'(X) ≥ r(X) for each Ø ≠ X ⊂ V, where dG(X) denotes the degree of a vertex set X' in G. This problem includes the edge-connectivity augmentation problem, and in general, it is NP-hard even if a polynomial time oracle for r is available. In this paper, we show that the problem can be solved in O(n4(m + n log n + q)) time, under the assumption that each Ø ≠ X ⊂ V satisfies r(X) ≥ 2 whenever r(X) 0, where n |V|, m = |{{u, v}| (u, v) ε E}|, and q is the time required to compute r(X) for each X ⊆ V.