Approximation Hardness of the Steiner Tree Problem on Graphs

Authors:
Miroslav Chlebík;Janka Chlebíková
Affiliations:
-;-
Venue:
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Year:
2002

Citing 6
Cited 22

The steiner problem with edge lengths 1 and 2,

Information Processing Letters
Some optimal inapproximability results

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the approximability of the traveling salesman problem (extended abstract)

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved Steiner tree approximation in graphs

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the Approximability of the Steiner Tree Problem

MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Proof verification and hardness of approximation problems

SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science

Polynomial time algorithms for network information flow

Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Complexity of approximating bounded variants of optimization problems

Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Playing push vs pull: models and algorithms for disseminating dynamic data in networks

Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
On routing in VLSI design and communication networks

Discrete Applied Mathematics
Aggregating Robots Compute: An Adaptive Heuristic for the Euclidean Steiner Tree Problem

SAB '08 Proceedings of the 10th international conference on Simulation of Adaptive Behavior: From Animals to Animats
A Faster Shortest-Paths Algorithm for Minor-Closed Graph Classes

Graph-Theoretic Concepts in Computer Science
Shortest paths in linear time on minor-closed graph classes, with an application to Steiner tree approximation

Discrete Applied Mathematics
On the Complexity of the Asymmetric VPN Problem

APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation hardness for small occurrence instances of NP-hard problems

CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
New geometry-inspired relaxations and algorithms for the metric steiner tree problem

IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Multicast routing in multi-radio multi-channel wireless mesh networks

IEEE Transactions on Wireless Communications
On the Approximability of Budgeted Allocations and Improved Lower Bounds for Submodular Welfare Maximization and GAP

SIAM Journal on Computing
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk

Mathematics of Operations Research
Dealing with large hidden constants: engineering a planar steiner tree PTAS

Journal of Experimental Algorithmics (JEA)
Sampling and Cost-Sharing: Approximation Algorithms for Stochastic Optimization Problems

SIAM Journal on Computing
Geometric network design with selfish agents

COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Implementation of approximation algorithms for the multicast congestion problem

WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Hypergraphic LP relaxations for steiner trees

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Fast local search for the steiner problem in graphs

Journal of Experimental Algorithmics (JEA)
A new point of NP-hardness for unique games

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the approximability of Dense Steiner Problems

Journal of Discrete Algorithms
A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

Steiner tree problem in weighted graphs seeks a minimum weight subtree containing a given subset of the vertices (terminals). We show that it is NP-hard to approximate the Steiner tree problem within 96/95. Our inapproximability results are stated in parametric way and can be further improved just providing gadgets and/or expanders with better parameters. The reduction is from H氓stad's inapproximability result for maximum satisfiability of linear equations modulo 2 with three unknowns per equation. This was first used for the Steiner tree problem by Thimm whose approach was the main starting point for our results.