Approximation algorithms for minimum-cost k-vertex connected subgraphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A primal-dual schema based approximation algorithm for the element connectivity problem
Journal of Algorithms
A primal-dual approximation algorithm for the survivable network design problem in hypergraphs
Discrete Applied Mathematics
Polynomial-Time Approximation Schemes for the Euclidean Survivable Network Design Problem
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A fast approximation scheme for fractional covering problems with variable upper bounds
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating connectivity augmentation problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
Approximate min--max theorems for Steiner rooted-orientations of graphs and hypergraphs
Journal of Combinatorial Theory Series B
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximating Steiner Networks with Node-Weights
SIAM Journal on Computing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
Efficient relay deployment for controlling connectivity in delay tolerant mobile networks
Proceedings of the 16th ACM international conference on Modeling, analysis & simulation of wireless and mobile systems
Hi-index | 0.01 |
In the survivable network design problem (SNDP), given an undirected graph and values rij for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are rij disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SNDP), the paths must be vertex disjoint. Jain et al. [12] propose a version of the problem intermediate in difficulty to these two, called the element connectivity problem (ELC-SNDP, or ELC). In this problem, the set of vertices is partitioned into terminals and nonterminals. The edges and nonterminals of the graph are called elements. The values rij are only specified for pairs of terminals i, j, and the paths from i to j must be element disjoint. Thus if rij - 1 elements fail, terminals i and j are still connected by a path in the network.These variants of SNDP are all known to be NP-hard. The best known approximation algorithm for the EC-SNDP has performance guarantee of 2 (due to Jain [11]), and iterativelyrounds solutions to a linear programming relaxation of the problem. ELC has a primal-dual O(log k)-approximation algorithm, where k = maxi,j rij (Jain et al. [12]). VC-SNDP is not known to have a non-trivial approximation algorithm; however, recently Fleischer [7] has shown how to extend the technique of Jain [11] to give a 2-approximation algorithm in the case that r ij \in赂 {0, 1, 2}. She also shows that the same techniques will not work for VC-SNDP for more general values of rij.In this paper we show that these techniques can be extended to a 2-approximation algorithm for ELC. This gives the first constant approximation algorithm for a general survivable network design problem which allows node failures.