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
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Approximating k-node Connected Subgraphs via Critical Graphs
SIAM Journal on Computing
Approximation Algorithms for Network Design with Metric Costs
SIAM Journal on Discrete Mathematics
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Inapproximability of survivable networks
Theoretical Computer Science
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
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An O(k^3 log n)-Approximation Algorithm for Vertex-Connectivity Survivable Network Design
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
Survivable network activation problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
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A subset T⊆V of terminals is k-connected to a root s in a directed/undirected graph J if J has k internally-disjoint vs-paths for every v∈T; T is k-connected in J if T is k-connected to every s∈T. We consider the Subsetk-Connectivity Augmentation problem: given a graph G=(V,E) with edge/node-costs, a node subset T⊆V, and a subgraph J=(V,EJ) of G such that T is (k−1)-connected in J, find a minimum-cost augmenting edge-set F⊆E∖EJ such that T is k-connected in J∪F. The problem admits trivial ratio O(|T|2). We consider the case |T|k and prove that for directed/undirected graphs and edge/node-costs, a ρ-approximation algorithm for Rooted Subsetk-Connectivity Augmentation implies the following approximation ratios for Subsetk-Connectivity Augmentation: (i) b(\rho+k) + {\left(\frac{|T|}{|T|-k}\right)}^2 O\left(\log \frac{|T|}{|T|-k}\right) and (ii) \rho \cdot O\left(\frac{|T|}{|T|-k} \log k \right), where b=1 for undirected graphs and b=2 for directed graphs. The best known values of ρ on undirected graphs are min {|T|,O(k)} for edge-costs and min {|T|,O(k log|T|)} for node-costs; for directed graphs ρ=|T| for both versions. Our results imply that unless k=|T|−o(|T|), Subsetk-Connectivity Augmentation admits the same ratios as the best known ones for the rooted version. This improves the ratios in [19,14].