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
STOC '97 Proceedings of the twenty-ninth 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
Minimum transversals in posi-modular systems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Graph Orientations with Set Connectivity Requirements
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Posi-modular Systems with Modulotone Requirements under Permutation Constraints
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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Given a graph G = (V, E) and a requirement function r: W1 x W2 → R+ for two families W1, W2 ⊆ 2V - {θ}, we consider the problem (called area-to-area edge-connectivity augmentation problem) of augmenting G by a smallest number of new edges so that the resulting graph G satisfies δG (X) ≥ r(W1, W2) for all X ⊆ V, W1 ∈ W1, and W2 ∈ W2 with W1 ⊆ X ⊆ V - W2, where δG(X) denotes the degree of a vertex set X in G. This problem can be regarded as a natural generalization of the global, local, and node-to-area edge-connectivity augmentation problems. In this paper, we show that there exists a constant c such that the problem is inapproximable within a ratio of clog α(W1, W2), unless P=NP, even restricted to the directed global node-to-area edge-connectivity augmentation or undirected local node-to-area edge-connectivity augmentation, where α(W1, W2) denotes the number of pairs W1 ∈ W1 and W2 ∈ W2 with r(W1, W2) 0. We also provide an O(log α (W1, W2))-approximation algorithm for the area-to-area edge-connectivity augmentation problem. This together with the negative result implies that the problem is Θ(log α (W1, W2))-approximable, unless P=NP, which solves open problems for node-to-area edge-connectivity augmentation (Ishii et al. 2008, Ishii and Hagiwara 2006, Miwa and Ito 2004). Furthermore, we characterize the node-to-area and area-to-area edge-connectivity augmentation problems as the augmentation problems with modulotone and extended modulotone functions.