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
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
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
Efficient recovery from power outage (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Constant Ratio Approximations of the Weighted Feedback Vertex Set Problem for Undirected Graphs
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
An 8-approximation algorithm for the subset feedback vertex set problem
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Approximation Algorithms for Constrained Node Weighted Steiner Tree Problems
SIAM Journal on Computing
The Steiner tree problem on graphs: Inapproximability results
Theoretical Computer Science
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
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
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
The Design of Approximation Algorithms
The Design of Approximation Algorithms
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
The node-weighted steiner problem in graphs of restricted node weights
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximation schemes for node-weighted geometric steiner tree problems
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Solving connected subgraph problems in wildlife conservation
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
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Node-Weighted Steiner Forest is the following problem: Given an undirected graph, a set of pairs of terminal vertices, a weight function on the vertices, find a minimum weight set of vertices that includes and connects each pair of terminals. We consider the restriction to planar graphs where the problem remains NP-complete. Demaine et al. showed that the generic primal-dual algorithm of Goemans and Williamson is a 6-approximation on planar graphs. We present (1) two different analyses to prove an approximation factor of 3, (2) show that our analysis is best possible for the chosen proof strategy, and (3) generalize this result to feedback problems on planar graphs. We give a simple proof for the first result using contraction techniques and following a standard proof strategy for the generic primal-dual algorithm. Given this proof strategy our analysis is best possible which implies that proving a better upper bound for this algorithm, if possible, would require different proof methods. Then, we give a reduction on planar graphs of Feedback Vertex Set to Node-Weighted Steiner Tree, and Subset Feedback Vertex Set to Node-Weighted Steiner Forest. This generalizes our result to the feedback problems studied by Goemans and Williamson. For the opposite direction, we show how our constructions can be combined with the proof idea for the feedback problems to yield an alternative proof of the same approximation guarantee for Node-Weighted Steiner Forest.