When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A primal-dual schema based approximation algorithm for the element connectivity problem
Journal of Algorithms
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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 Steiner Networks with Node-Weights
SIAM Journal on Computing
Primal-dual approximation algorithms for node-weighted steiner forest on planar graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Survivable network design problems in wireless networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G=(V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each pair uv, H contains r(uv) edge-disjoint paths between u and v. Our main result is an O(k)-approximation algorithm for EC-SNDP where k= max uvr(uv) is the maximum requirement. This improves the O(k logn)-approximation known for node-weighted EC-SNDP in general graphs [15]. Our algorithm and analysis applies to the more general problem of covering a proper function with maximum requirement k. Our result is inspired by, and generalizes, the work of Demaine, Hajiaghayi and Klein [5] who gave constant factor approximation algorithms for node-weighted Steiner tree and Steiner forest problems (and more generally covering 0-1 proper functions) in planar and minor-closed families of graphs.