Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Scan-first search and sparse certificates: an improved parallel algorithm for k-vertex connectivity
SIAM Journal on Computing
A minimum 3-connectivity augmentation of a graph
Journal of Computer and System Sciences
On the optimal vertex-connectivity augmentation
Journal of Combinatorial Theory Series B
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
A note on the vertex-connectivity augmentation problem
Journal of Combinatorial Theory Series B
Fast algorithms for k-shredders and k-node connectivity augmentation
Journal of Algorithms
On four-connecting a triconnected graph
Journal of Algorithms
On the Minimum Augmentation of an l-Connected Graph to a k-Connected Graph
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Augmenting Edge and Vertex Connectivities Simultaneously
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Undirected Vertex-Connectivity Structure and Smallest Four-Vertex-Connectivity Augmentation
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Optimal Augmentation for Bipartite Componentwise Biconnectiviy in Linear Time (Extended Abstract)
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Approximating Node-Connectivity Augmentation Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
An algorithm for (n-3)-connectivity augmentation problem: Jump system approach
Journal of Combinatorial Theory Series B
Augmenting forests to meet odd diameter requirements
Discrete Optimization
An overview of algorithms for network survivability
ISRN Communications and Networking
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Given an undirected graph G and a positive integer k, the k-vertex-connectivity augmentation problem is to find a smallest set F of new edges for which G + F is k-vertex-connected. Polynomial algorithms for this problem are known only for k ≤ 4 and a major open question in graph connectivity is whether this problem is solvable in polynomial time in general. For arbitrary k, a previous result of Jordán [14] gives a polynomial algorithm which adds an augmenting set F of size at most k - 3 more than the optimum, provided G is (k - 1)-vertex-connected. In this paper we develop a polynomial algorithm which makes an l- connected graph G k-vertex-connected by adding an augmenting set of size at most ((k - l)(k - 1) + 4)=2 more than (a new lower bound for) the optimum. This extends the main results of [14,15]. We partly follow and generalize the approach of [14] and we adapt the splitting off method (which worked well on edge-connectivity augmentation problems) to vertex-connectivity. A key point in our proofs, which may also find applications elsewhere, is a new tripartite submodular inequality for the sizes of neighbour-sets in a graph.