# Discovering Treewidth

@inproceedings{Bodlaender2005DiscoveringT, title={Discovering Treewidth}, author={Hans L. Bodlaender}, booktitle={SOFSEM}, year={2005} }

Treewidth is a graph parameter with several interesting theoretical and practical applications. This survey reviews algorithmic results on determining the treewidth of a given graph, and finding a tree decomposition of small width. Both theoretical results, establishing the asymptotic computational complexity of the problem, as experimental work on heuristics (both for upper bounds as for lower bounds), preprocessing, exact algorithms, and postprocessing are discussed.

## 189 Citations

### Treewidth: Characterizations, Applications, and Computations

- Computer ScienceWG
- 2006

This paper gives a short survey on algorithmic aspects of the treewidth of graphs, with an emphasis on algorithms that have been experimentally tested.

### Treewidth, Tree Decompositions, and Brambles

- Computer Science
- 2011

The most important results for treewidth, tree decompositions, and brambles are reviewed, both from a theoretical and practical point of view.

### A Branch and Bound Algorithm for Exact, Upper, and Lower Bounds on Treewidth

- Computer ScienceAAIM
- 2006

It is discussed how the algorithm can not only be used to obtain exact bounds for the treewidth, but also to obtain upper and/or lower bounds.

### Treewidth Lower Bounds with Brambles

- Computer Science, MathematicsAlgorithmica
- 2007

Two algorithms are given: one for general graphs, and one for planar graphs that are shown to give a lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum.

### New Upper Bound Heuristics for Treewidth

- BusinessWEA
- 2005

In this paper, some heuristics to find an upper bound on the treewidth of a given graph are introduced and evaluated and in several cases, the newHeuristics improve the bounds obtained by existing heuristic.

### Treewidth: Structure and Algorithms

- Computer ScienceSIROCCO
- 2007

The interaction between different characterizations of the graph theoretic notion of treewidth, and algorithms and algorithmic applications, is looked at.

### Treewidth and Dynamic Programming

- Computer Science
- 2013

This chapter is devoted to developing the basic theory oftreewidth, and fundamental aspects of producing treewidth algorithms by running dynamic programming on graphs.

### A Local Search Algorithm for Branchwidth

- MathematicsSOFSEM
- 2011

The first local search algorithm for branch decompositions of small width of given graphs is given using non-trivial combinatorial properties of the neighbourhood space, and it is shown that significant reductions in the search space can be obtained.

### Duplicate Avoidance in Depth-First Search with Applications to Treewidth

- Computer ScienceIJCAI
- 2009

A duplicate avoidance technique is developed and it is demonstrated that it significantly outperforms other algorithms when memory is limited and is able to find, for the first time, the treewidth of several hard benchmark graphs.

## References

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A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find tree-decompositions, algorithms that…

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A new lower bound for the treewidth (and hence the pathwidth) of a graph is presented and a linear-time algorithm is given to compute the bound.

### Treewidth Lower Bounds with Brambles

- Computer Science, MathematicsAlgorithmica
- 2007

Two algorithms are given: one for general graphs, and one for planar graphs that are shown to give a lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum.

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We show that for a graph G on n vertices its treewidth and minimum fill-in can be computed roughly in 1.9601 n time. Our result is based on a combinatorial proof that the number of minimal separators…

### New Upper Bound Heuristics for Treewidth

- BusinessWEA
- 2005

In this paper, some heuristics to find an upper bound on the treewidth of a given graph are introduced and evaluated and in several cases, the newHeuristics improve the bounds obtained by existing heuristic.

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Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs, and it is shown that unless P = NP there are no absolute approximation algorithms for any of the parameters.

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New lower and upper bounds for the treewidth are proposed and tested on the well known DIMACS benchmark for graph coloring, and the heuristic method computes good bounds within a very small computing time.