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
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Augmenting edge-connectivity between vertex subsets
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
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For a finite ground set V, we call a set-function r:2^V-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:2^V-Z^+, we consider the problem of augmenting G by a smallest number of new edges, so that the resulting graph G^' satisfies d"G"^"'(X)=r(X) for each 0@?X@?V, where d"G(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(n^4(m+nlogn+q)) time, under the assumption that each 0@?X@?V satisfies r(X)=2 whenever r(X)0, where n=|V|, m=|{{u,v}|(u,v)@?E}|, and q is the time required to compute r(X) for each X@?V.