The steiner problem with edge lengths 1 and 2,
Information Processing Letters
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
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
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
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete 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
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Black-box reductions for cost-sharing mechanism design
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating rooted Steiner networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Approximability of 3- and 4-hop bounded disjoint paths problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We study the survivable network design problem (SNDP) for vertex connectivity. Given a graph G(V,E) with costs on edges, the goal of SNDP is to find a minimum cost subset of edges that ensures a given set of pairwise vertex connectivity requirements. When all connectivity requirements are between a special vertex, called the source, and vertices in a subset T ⊆ V, called terminals, the problem is called the single-source SNDP. Our main result is a randomized kO(k2) log4n-approximation algorithm for single-source SNDP where k denotes the largest connectivity requirement for any source-terminal pair. In particular, we get a poly-logarithmic approximation for any constant k. Prior to our work, no non-trivial approximation guarantees were known for this problem for any k ≥ 3. We also show that SNDP is kΩ(1)-hard to approximate and provide an elementary construction that shows that the well-studied set-pair linear programming relaxation for this problem has an Ω(k1/3) integrality gap.