Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete 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
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Approximation Algorithms for Network Design with Metric Costs
SIAM Journal on Discrete Mathematics
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
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
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
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 LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating subset k-connectivity problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Approximating subset k-connectivity problems
Journal of Discrete Algorithms
| Hi-index | 0.00 |
The minimum-cost subset k-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph G = (V,E) with costs on edges and a set of terminals T. The goal is to find a minimum cost subgraph such that every pair of terminals are connected by k openly (vertex) disjoint paths. In this paper, we present an approximation algorithm for the subset k-connected subgraph problem which improves on the previous best approximation guarantee of O(k2 log k) by Nutov (FOCS 2009). Our approximation guarantee, α(|T|), depends upon the number of terminals: α(|T|) = {O(|T|2) if|T| k O(k log2 k) if2k ≤ |T| k2 O(k log k) if|T| ≥ k2 So, when the number of terminals is large enough, the approximation guarantee improves significantly. Moreover, we show that, given an approximation algorithm for |T| = k, we can obtain almost the same approximation guarantee for any instances with |T| k. This suggests that the hardest instances of the problem are when |T| ≈ k.