# A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions

@inproceedings{Bosman2015ASM, title={A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions}, author={Thomas Bosman}, booktitle={SEA}, year={2015} }

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of treewidth sufficiently small to make these al- gorithms fast enough for practical use. Consequently, tree decomposition based algorithms have limited applicability to large scale optimization. However, by first reducing the input graph so that a small width tree…

## 6 Citations

A Variable Neighborhood Search Algorithm for Solving the Steiner Minimal Tree Problem

- Computer ScienceICCASA/ICTCC
- 2018

The proposed variable neighborhood search (VNS) algorithm for solving the SMT problem has been tested on sparse graphs in a standardized experimental data system, and it yields better results than some other heuristic algorithms.

Application of SMT problem EAI Endorsed Transactions on Context-aware Systems and Applications Research

- Computer Science
- 2019

The proposed Variable Neighborhood Search (VNS) algorithm for solving the SMT problem in sparse graphs yields better results than some other heuristic algorithms.

Technical Report Column

- Computer ScienceSIGA
- 2015

The quantitative relation between VC- dimension and two other basic parameters related to learning and teaching are studied, including the quality of sample compression schemes and of teaching sets for classes of low VC-dimension.

Strain-aware assembly of genomes from mixed samples using variation graphs

- Computer SciencebioRxiv
- 2019

This work provides a referencegenome-independent solution based on the construction of a variation graph, capturing all diversity present in the sample and solves the contig abundance estimation problem and proposes a greedy algorithm to efficiently build maximal-length haplotypes.

Viral quasispecies reconstruction via contig abundance estimation in variation graphs

- Engineering
- 2019

This work provides a reference-genome-independent solution based on the construction of a variation graph, capturing all quasispecies diversity present in the sample and solves the contig abundance estimation problem and proposes a greedy algorithm to efficiently build full-length haplotypes.

Strain-Aware Assembly of Genomes from Mixed Samples Using Flow Variation Graphs

- BiologyRECOMB
- 2020

The goal of strain-aware genome assembly is to reconstruct all individual haplotypes from a mixed sample at the strain level and to provide abundance estimates for the strains.

## References

SHOWING 1-10 OF 12 REFERENCES

Speeding Up Dynamic Programming with Representative Sets - An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

- Computer ScienceIPEC
- 2013

Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth and the central idea is that it suffices to compute representative sets, and these can be computed efficiently with help of Gaussian elimination.

Algorithms for the Steiner problem in networks

- Computer Science, Mathematics
- 2003

The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost, a classical NP-hard problem with many important applications and several new techniques are developed, implemented and test.

On exact algorithms for treewidth

- Computer ScienceTALG
- 2012

Experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential-time algorithms using exponential space or using only polynomial space are given and it is shown that with a more complicated algorithm using balanced separators, Treewidth can be computed in O*(2.9512n) time and polynometric space.

Tour Merging via Branch-Decomposition

- Computer ScienceINFORMS J. Comput.
- 2003

A heuristic method for finding branch decompositions based on the eigenvector technique for finding graph separators is described; this is used as a tool to obtain high-quality tours for the traveling salesman problem by merging collections of tours produced by standard traveling salesman heuristics.

SteinLib: An Updated Library on Steiner Tree Problems in Graphs

- Computer Science, Mathematics
- 2001

The SteinLib is presented, a library of data sets for the Steiner tree problem in graphs that extends former libraries on Steiners tree problems by many new interesting and difficult instances, most of them arising from real-world applications.

A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs

- MathematicsINFORMS J. Comput.
- 2002

A hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP + PR) for the Steiner problem in graphs is proposed and described, which is very competitive when compared to other approximate algorithms.

Treewidth computations I

- Upper bounds, Information and Computation 208, 259-275
- 2010

Treewidth computations I. Upper bounds, Information and Computation

- Treewidth computations I. Upper bounds, Information and Computation
- 2010