Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Undirected Vertex-Connectivity Structure and Smallest Four-Vertex-Connectivity Augmentation
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the minimum local-vertex-connectivity augmentation in graphs
Discrete Applied Mathematics
Minimum augmentation of edge-connectivity with monotone requirements in undirected graphs
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
The Set Connector Problem in Graphs
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
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
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
A note on Rooted Survivable Networks
Information Processing Letters
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
Approximating connectivity augmentation problems
ACM Transactions on Algorithms (TALG)
Note: Local edge-connectivity augmentation in hypergraphs is NP-complete
Discrete Applied Mathematics
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Augmenting edge-connectivity between vertex subsets
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Let G = (V, E) be a graph and let S ⊆ V. The S-connectivity λs(u, v; G) of u and v in G is the maximum number of uv-paths that no two of them have an edge or a node in S - {u, v} in common. The corresponding Connectivity Augmentation Problem (CAP) is: given a graph G = (V, E), a node subset S ⊆ V, and a nonnegative integer requirement function r(u, v) on the set of pairs of nodes, add a minimum size set F of new edges to G so that λs(u, v; G + F) ≥ r(u, v) holds for all u, v ∈ V. Three extensively studied particular cases are: the edge- (S = θ), the node- (S = V), and the element- (r(u, v) = 0 whenever u ∈ S or v ∈ S) CAP. A polynomial algorithm for edge- CAP was developed by A. Frank [8]. In this paper we consider the element-CAP and the node-CAP, that are NP- hard even for r(u, v) ∈ {0, 2}. Our main result is a 7/4- approximation algorithm for the element-CAP, improving the previously best known 2-approximation. For the {0, k}- element-CAP (with r(u, v) ∈ {0, k}) and for the {0, 1, 2}-element-CAP we give a 3/2-approximation algorithm. The approximation ratios are based on a new lower bound on the number of edges needed to cover a skew-supermodular set function. For the node-CAP we establish the following approximation threshold: the {0, k}-node-CAP cannot be approximated within O(2log-1-∈n) for any fixed ∈ 0, unless NP ⊆ DTIME(nPolylog(n)); thus the node-CAP is unlikely to have a polylogarithmic approximation.