# An improved LP-based approximation for steiner tree

@inproceedings{Byrka2010AnIL, title={An improved LP-based approximation for steiner tree}, author={Jaroslaw Byrka and Fabrizio Grandoni and Thomas Rothvoss and Laura Sanit{\`a}}, booktitle={STOC '10}, year={2010} }

The Steiner tree problem is one of the most fundamental NP-hard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum-cost tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from 2 to the current best 1.55 [Robins,Zelikovsky-SIDMA'05]. All these algorithms are purely combinatorial. A long-standing open problem is whether there is an LP-relaxation for Steiner tree with integrality gap smaller than 2…

## 292 Citations

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.

Computing Optimal Steiner Trees in Polynomial Space

- Computer Science, MathematicsAlgorithmica
- 2012

This paper presents a O(1.55n)-time polynomial-space algorithm for the cardinality version of the Steiner tree problem, where all edge weights are one, and a improved branching strategy based on a improved branch strategy.

On Extended Formulations For Parameterized Steiner Trees

- Mathematics, Computer ScienceIPEC
- 2021

It is proved that Steiner Tree admits an integral LP with O (3 k | E | ) variables and constraints, which matches the runtime of the Dreyfus-Wagner algorithm, and the poof gives a polyhedral perspective on this classic algorithm.

An Improved Approximation Ratio to the Partial-Terminal Steiner Tree Problem

- Mathematics, Computer ScienceIEEE Transactions on Computers
- 2015

This paper improves the ratio from 2ρ to 2ρ- [(ρ)/(3ρ- 2)] - f, where f is a non-negative function whose value is between 0 and ρ- [( ρ)/( 3ρ-2)].

Online Node-Weighted Steiner Tree and Related Problems

- Computer Science, Mathematics2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
- 2011

This work designs polynomial-time online algorithms with poly-logarithmic competitive ratios for two fundamental network design problems in edge-weighted graphs and designs new LP formulations for these problems drawing on a combination of paradigms.

Improved Approximation Algorithm for the ( 1 , 2 )-Partial-Terminal Steiner Tree Problem

- Computer Science, Mathematics
- 2014

A polynomialtime approximation algorithm is proposed that improves the approximation ratio of PTSTP(1,2) from 1.79 to 1.67.

An Integral Linear Programming Relaxation for Parameterized Steiner Trees

- Mathematics, Computer Science
- 2019

A novel linear program (LP) for the Steiner Tree problem, where a set of terminal vertices need to be connected by a minimum weight tree in an edge-weighted graph, which shows that the problem admits an integral LP with 3|E| variables and 2|V | constraints.

An improved approximation algorithm for the partial-terminal Steiner tree problem with edge cost 1 or 2

- Computer Science, MathematicsJ. Discrete Algorithms
- 2015

A Primal-Dual based Distributed Approximation Algorithm for Prize Collecting Steiner Tree

- Computer Science, MathematicsDiscret. Math. Algorithms Appl.
- 2021

A distributed algorithm that constructs a prize collecting steiner tree for a given connected undirected graph with non- negative weight for each edge and non-negative prize value for each node and achieves an approximation factor of 2 of the optimal.

An FPTAS for the fractional group Steiner tree problem

- Mathematics, Computer Science
- 2015

This paper considers a linear relaxation of the cut-based integer programming formulation for the group Steiner tree problem (FGST). We combine the approach of Koufogiannakis and Young (2013) with…

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