A polynomial algorithm for b-matchings: an alternative approach
Information Processing Letters
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A faster strongly polynomial minimum cost flow algorithm
Operations Research
On the optimal vertex-connectivity augmentation
Journal of Combinatorial Theory Series B
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
A representation for crossing set families with applications to submodular flow problems
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Power optimization in ad hoc wireless network topology control with biconnectivity requirements
Computers and Operations Research
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We generalize and unify techniques from several papers to obtain relatively simple and general technique for designing approximation algorithms for finding min-cost k-node connected spanning subgraphs. For the general instance of the problem, the previously best known algorithm has approximation ratio 2k. For k ≤ 5, algorithms with approximation ratio ⌈(k+1)/2⌉ are known. For metric costs Khuller and Raghavachari gave a (2 + 2(k-1/n))-approximation algorithm. We obtain the following results. (i) An I(k-k0)-approximation algorithm for the problem of making a k0-connected graph k-connected by adding a minimum cost edge set, where I(k) = 2++⌊k/2⌋-1 j=1 1/j ⌊k/j+1⌋. (ii) A (2 + k-1/n)-approximation algorithm for metric costs. (iv) A ⌊(k + 1)/2⌋-approximation algorithm for k = 6, 7. (v) A fast ⌊(k + 1)/2⌋-approximation algorithm for k = 4. The multiroot problem generalizes the min-cost k-connected subgraph problem. In the multiroot problem, requirements ku for every node u are given, and the aim is to find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u,v. For the general instance of the problem, the best known algorithm has approximation ratio 2k, where k = maxku. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for k ≤ 7 the approximation guarantee from 3 to 2 + ⌊(k - 1)/2⌋/k