A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
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
Power optimization for connectivity problems
Mathematical Programming: Series A and B
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
Algorithms for Single-Source Vertex Connectivity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Rooted k-connections in digraphs
Discrete Applied Mathematics
A note on Rooted Survivable Networks
Information Processing Letters
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On minimum power connectivity problems
Journal of Discrete Algorithms
Approximating minimum power covers of intersecting families and directed edge-connectivity problems
Theoretical Computer Science
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating Steiner Networks with Node-Weights
SIAM Journal on Computing
Survivable network design problems in wireless networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximating subset k-connectivity problems
Journal of Discrete Algorithms
Hi-index | 5.23 |
In the Survivable Networks Activation problem we are given a graph G=(V,E), S@?V, a family {f^u^v(x"u,x"v):uv@?E} of monotone non-decreasing activating functions from R"+^2 to {0,1} each, and connectivity requirements{r(uv):uv@?R} over a set R of requirement edges on V. The goal is to find a weight assignmentw={w"v:v@?V} of minimum total weight w(V)=@?"v"@?"Vw"v, such that in the activated graphG"w=(V,E"w), where E"w={uv:f^u^v(w"u,w"v)=1}, the following holds: for each uv@?R, the activated graph G"w contains r(uv) pairwise edge-disjoint uv-paths such that no two of them have a node in S@?{u,v} in common. This problem was suggested recently by Panigrahi (2011) [19], generalizing the Node-Weighted Survivable Network and the Minimum-Power Survivable Network problems, as well as several other problems with motivation in wireless networks. We give new approximation algorithms for this problem. For undirected/directed graphs, our ratios are O(klogn) for k-Out/In-connected Subgraph Activation and k-Connected Subgraph Activation. For directed graphs this solves a question from Panigrahi (2011) [19] for k=1, while for the min-power case and k arbitrary this solves a question from Nutov (2010) [16]. For other versions on undirected graphs, our ratios match the best known ones for the Node-Weighted Survivable Network problem (Nutov, 2009 [14]).