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
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Combinatorial optimization
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for constrained for constrained node weighted steiner tree problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Power optimization for connectivity problems
Mathematical Programming: Series A and B
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Inapproximability of survivable networks
Theoretical Computer Science
Approximating Some Network Design Problems with Node Costs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximating connectivity augmentation problems
ACM Transactions on Algorithms (TALG)
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximating minimum power covers of intersecting families and directed edge-connectivity problems
Theoretical Computer Science
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Survivable network activation problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Node-weighted network design in planar and minor-closed families of graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Survivable network activation problems
Theoretical Computer Science
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The (undirected) Steiner Network problem is as follows: given a graph $G=(V,E)$ with edge/node-weights and edge-connectivity requirements $\{r(u,v):u,v\in U\subseteq V\}$, find a minimum-weight subgraph $H$ of $G$ containing $U$ so that the $uv$-edge-connectivity in $H$ is at least $r(u,v)$ for all $u,v\in U$. The seminal paper of Jain [Combinatorica, 21 (2001), pp. 39-60], and numerous papers preceding it, considered the Edge-Weighted Steiner Network problem, with weights on the edges only, and developed novel tools for approximating minimum-weight edge-covers of several types of set functions and families. However, for the Node-Weighted Steiner Network (NWSN) problem, nontrivial approximation algorithms were known only for $0,1$ requirements. We make an attempt to change this situation by giving the first nontrivial approximation algorithm for NWSN with arbitrary requirements. Our approximation ratio for NWSN is $r_{\max}\cdot O(\ln|U|)$, where $r_{\max}=\max_{u,v\in U}r(u,v)$. This generalizes the result of Klein and Ravi [J. Algorithms, 19 (1995), pp. 104-115] for the case $r_{\max}=1$. We also give an $O(\ln|U|)$-approximation algorithm for the node-connectivity variant of NWSN (when the paths are required to be internally disjoint) for the case $r_{\max}=2$. Our results are based on a much more general approximation algorithm for the problem of finding a minimum node-weighted edge-cover of an uncrossable set-family. Finally, we give evidence that a polylogarithmic approximation ratio for NWSN with large $r_{\max}$ might not exist even for $|U|=2$ and unit weights.