Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
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
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
An approximation algorithm for minimum-cost vertex-connectivity problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On approximability of the minimum-cost k-connected spanning subgraph problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computing vertex connectivity: new bounds from old techniques
Journal of Algorithms
Erratum: an approximation algorithm for minimum-cost vertex-connectivity problems
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching
SIAM Journal on Computing
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximation algorithm for k-node connected subgraphs via critical graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating the smallest k-edge connected spanning subgraph by LP-rounding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
Using expander graphs to find vertex connectivity
Journal of the ACM (JACM)
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximating Minimum-Power k-Connectivity
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating minimum-power edge-covers and 2,3-connectivity
Discrete Applied Mathematics
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating survivable networks with minimum number of Steiner points
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
An improved approximation algorithm for minimum-cost subset k-connectivity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Survivable network activation problems
Theoretical Computer Science
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We present an O(log n• log k)-approximation algorithm for the problem of finding k-vertex connected spanning subgraph of minimum cost, where n is the number of vertices in the input graph, and k is the connectivity requirement. Our algorithm works for both directed and undirected graphs. The best known approximation guarantees for these problems are O(ln k• min{√k,n/n-k ln k}) by Kortsarz and Nutov, and O(ln{k}) in the case of undirected graphs where n≥ 6k2 by Cheriyan, Vempala, and Vetta. Our algorithm is the first that has a polylogarithmic guarantee for all values of k. Combining our algorithm with the algorithm of Kortsarz and Nutov in case of small k, e.g., k2 k)-approximation algorithm. As in previous work, we use the Frank-Tardos algorithm for finding k-outconnected subgraphs as a subroutine. However, with a structural lemmas that we proved, we are able to show that we need only partial solutions returned by the Frank-Tardos algorithm; thus, we can avoid paying the whole cost of the optimal solution every time the algorithm is applied.