When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Connectivity and network flows
Handbook of combinatorics (vol. 1)
The Euclidean Bottleneck Steiner Tree and Steiner Tree with Minimum Number of Steiner Points
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Deploying sensor networks with guaranteed capacity and fault tolerance
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Approximating k-node Connected Subgraphs via Critical Graphs
SIAM Journal on Computing
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
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Wireless network design via 3-decompositions
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
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximating minimum-power degree and connectivity problems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Relay placement for two-connectivity
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part II
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Given a graph H = (U,E) and connectivity requirements r = {r(u, v) : u, v ∈ R ⊆ U}, we say that H satisfies r if it contains r(u, v) pairwise internally-disjoint uv-paths for all u, v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space (M, ∥ċ∥), and connectivity requirements, find a minimum size set S ⊂ M - V of additional points, such that the unit disc graph induced by V ∪ S satisfies the requirements. In the (node-connectivity version of the) Survivable Network Design Problem (SNDP) we are given a graph G = (V, E) with edge costs and connectivity requirements, and seek a min-cost subgraph H of G that satisfies the requirements. Let k = maxu, v ∈ V r(u, v) denote the maximum connectivity requirement. We will show a natural transformation of an SN-MSP instance (V, r) into an SNDP instance (G = (V, E), c, r), such that an α-approximation for the SNDP instance implies an αċO(k2)- approximation algorithm for the SN-MSP instance. In particular, for the most interesting case of uniform requirement r(u, v) = k for all u, v ∈ V, we obtain for SN-MSP the ratio O(k2 ln k), which solves an open problem from [3].