Steiner Tree 1.39-Approximation in Practice

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8934)

Abstract

We consider the currently strongest Steiner tree approximation algorithm that has recently been published by Goemans, Olver, Rothvoß and Zenklusen (2012). It first solves a hypergraphic LP relaxation and then applies matroid theory to obtain an integral solution. The cost of the resulting Steiner tree is at most \((1.39 + \varepsilon )\)-times the cost of an optimal Steiner tree where \(\varepsilon \) tends to zero as some parameter \(k\) tends to infinity. However, the degree of the polynomial running time depends on this constant \(k\), so only small \(k\) are tractable in practice.

The algorithm has, to our knowledge, not been implemented and evaluated in practice before. We investigate different implementation aspects and parameter choices of the algorithm and compare tuned variants to an exact LP-based algorithm as well as to fast and simple \(2\)-approximations.

Keywords

Short Path Approximation Ratio Minimum Span Tree Steiner Tree Steiner Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of OsnabrückOsnabrückGermany

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