# Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs

@article{Moldenhauer2013PrimaldualAA, title={Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs}, author={Carsten Moldenhauer}, journal={Inf. Comput.}, year={2013}, volume={222}, pages={293-306} }

## 10 Citations

Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs

- Computer Science, MathematicsSWAT
- 2016

A new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm is given which establishes a new best approximation guarantee for planar NWPCST.

Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs

- Computer Science, MathematicsTALG
- 2013

An O(log n polyloglog n) approximation algorithm is obtained for the special case where the graph is planar embedded and each group is the set of nodes on a face, and the same approximation ratio is obtain for the minimum-weight tour that must visit each group.

Approximating Node-Weighted k-MST on Planar Graphs

- Computer ScienceTheory of Computing Systems
- 2020

It is argued that the bound is essentially best possible among algorithms that utilize an LMP algorithm for the Lagrangian relaxation as a black box, and can be interpreted as a generalization of an analogous result by Könemann et al. (Algorithmica ’11) for partial cover problems.

Node-Weighted Prize Collecting Steiner Tree and Applications

- Computer Science
- 2013

A new algorithm is proposed which is more involved and introduces novel ideas in primal dual approach for network design problems and it is shown how this property can be utilized to design an O(log n)-approximation algorithm for the Node-Weighted Quota Steiner Tree problem using the Lagrangian Relaxation method.

A Constant-Factor Approximation for Quasi-bipartite Directed Steiner Tree on Minor-Free Graphs

- Mathematics, Computer ScienceArXiv
- 2021

The first constant-factor approximation algorithm for quasi-bipartite instances of D IRECTED S TEINER T REE on graphs that exclude minors is given, using the primal-dual scheme.

Online Node-Weighted Steiner Forest and Extensions via Disk Paintings

- Mathematics, Computer Science2013 IEEE 54th Annual Symposium on Foundations of Computer Science
- 2013

The central idea in this technique is to amortize the cost of primal updates to a set of carefully selected mutually disjoint fixed-radius dual disks centered at a subset of terminals to form a new framework for online network design problems that is called disk paintings.

Hitting Weighted Even Cycles in Planar Graphs

- MathematicsAPPROX-RANDOM
- 2021

The main result is a primal-dual algorithm that yields a 47/7 ≈ 6.71-approximation for ECT on node-weighted planar graphs, and an integrality gap of the same value for the standard LP relaxation on nodes- WeightedPlanar graphs.

Node-weighted Network Design in Planar and Minor-closed Families of Graphs

- Mathematics, Computer ScienceICALP
- 2012

The main result is an O(k)-approximation algorithm for EC-SNDP and Elem- SNDP when the input graph is planar or more generally if it belongs to a proper minor-closed family of graphs; here, k = max uvr(uv) is the maximum connectivity requirement.

A reliable two-tier energy-efficient topology building algorithm for Wireless Sensor Networks

- Computer Science2014 Applications and Innovations in Mobile Computing (AIMoC)
- 2014

A reliable energy-efficient topology control algorithm in wireless sensor networks is proposed which not only balances the energy load of each node but also provides global reliability for the whole network.

Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs

- MathematicsAPPROX-RANDOM
- 2012

We present primal-dual algorithms which give a 2.4 approximation for a class of node-weighted network design problems in planar graphs, introduced by Demaine, Hajiaghayi and Klein (ICALP’09). This…

## References

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Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs

- Computer Science, MathematicsTALG
- 2013

An O(log n polyloglog n) approximation algorithm is obtained for the special case where the graph is planar embedded and each group is the set of nodes on a face, and the same approximation ratio is obtain for the minimum-weight tour that must visit each group.

Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs

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This work gives a ]-approxlmation algorithm for the general problem in planar graphs, given that the subset of cycles obeys certain properties, and uses the primaldual method for approximation algorithms as given in Goemans and Williamson.

Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth

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It is shown that Steiner forest can be solved in polynomial time for series-parallel graphs (graphs of treewidth at most two) by a novel combination of dynamic programming and minimum cut computations, completing the thorough complexity study of Steiner Forest in the range of bounded-treewidth graphs, planar graphs, and bounded-genus graphs.

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This paper improves the approximation factor for Steiner tree, developing an LP-based approximation algorithm based on a, seemingly novel, iterative randomized rounding technique and shows that the integrality gap of the LP is at most $1.55, hence answering to the mentioned open question.

Approximation Algorithms for Constrained Node Weighted Steiner Tree Problems

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This work considers a class of optimization problems where the input is an undirected graph with two weight functions defined for each node, namely the node's profit and its cost, and presents approximation algorithms for three natural optimization criteria that arise in this context.

Prize-collecting Steiner problems on planar graphs

- Mathematics, Computer ScienceSODA '11
- 2011

The first provable hardness separation between the approximability of a problem and its prize-collecting version is given, and it is shown that PCSF is APX-hard on Euclidean instances.

The Steiner tree problem on graphs: Inapproximability results

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Solving Connected Subgraph Problems in Wildlife Conservation

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It is shown that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the Connected Subgraph Problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow.

The Rectilinear Steiner Tree Problem in NP Complete

- MathematicsSIAM Journal of Applied Mathematics
- 1977

The problem of determining the minimum length of an optimum rectilinear Steiner tree for a set A of points in the plane is shown to be NP-complete and the emphasis of the literature on heuristics and special case algorithms is well justified.

A Nearly Best-Possible Approximation Algorithm for Node-Weighted Steiner Trees

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We give the first approximation algorithm for the node-weighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless $\tilde P \supseteq NP$. Our…