Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
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
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
A note on the vertex-connectivity augmentation problem
Journal of Combinatorial Theory Series B
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Approximation algorithms for minimum-cost k-vertex connected subgraphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Near Optimal Algorithm for Vertex Connectivity Augmentation
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Approximation algorithms for network design with metric costs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximating connectivity augmentation problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
Approximating k-node Connected Subgraphs via Critical Graphs
SIAM Journal on Computing
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
On shredders and vertex connectivity augmentation
Journal of Discrete Algorithms
An o(log2 k)-approximation algorithm for the k-vertex connected spanning subgraph problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
Inapproximability of Survivable Networks
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Algorithms for Single-Source Vertex Connectivity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating subset k-connectivity problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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We consider the (undirected) Node Connectivity Augmentation (NCA) problem: given a graph J = (V ,E J ) and connectivity requirements {r (u ,v ):u ,v *** V }, find a minimum size set I of new edges (any edge is allowed) so that J + I contains r (u ,v ) internally disjoint uv -paths, for all u ,v *** V . In the Rooted NCA there is s *** V so that r (u ,v ) 0 implies u = s or v = s . For large values of k = max u ,v *** V r (u ,v ), NCA is at least as hard to approximate as Label-Cover and thus it is unlikely to admit a polylogarithmic approximation. Rooted NCA is at least as hard to approximate as Hitting-Set. The previously best approximation ratios for the problem were O (k ln n ) for NCA and O (ln n ) for Rooted NCA. In [Approximating connectivity augmentation problems, SODA 2005] the author posed the following open question: Does there exist a function ρ (k ) so that NCA admits a ρ (k )-approximation algorithm? In this paper we answer this question, by giving an approximation algorithm with ratios O (k ln 2 k ) for NCA and O (ln 2 k ) for Rooted NCA. This is the first approximation algorithm with ratio independent of n , and thus is a constant for any fixed k . Our algorithm is based on the following new structural result which is of independent interest. If ${\cal D}$ is a set of node pairs in a graph J , then the maximum degree in the hypergraph formed by the inclusion minimal tight sets separating at least one pair in ${\cal D}$ is O (***2), where *** is the maximum connectivity of a pair in ${\cal D}$.