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
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Approximation algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
The Directed Steiner Network Problem Is Tractable for a Constant Number of Terminals
SIAM Journal on Computing
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algorithms for Single-Source Vertex Connectivity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Inapproximability of survivable networks
Theoretical Computer Science
A note on Rooted Survivable Networks
Information Processing Letters
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Approximating subset k-connectivity problems
Journal of Discrete Algorithms
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The Directed Steiner Tree (DST) problem is a cornerstone problem in network design. We focus on the generalization of the problem with higher connectivity requirements. The problem with one root and two sinks is APX-hard. The problem with one root and many sinks is as hard to approximate as the directed Steiner forest problem, and the latter is well known to be as hard to approximate as the label cover problem. Utilizing previous techniques (due to others), we strengthen these results and extend them to undirected graphs. Specifically, we give an Ω(kε) hardness bound for the rooted k-connectivity problem in undirected graphs; this addresses a recent open question of Khanna. As a consequence, we also obtain the Ω(kε) hardness of the undirected subset k-connectivity problem. Additionally, we give a result on the integrality ratio of the natural linear programming relaxation of the directed rooted k-connectivity problem.