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. 

Treewidth computations I. Upper bounds

Treewidth: Characterizations, Applications, and Computations

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

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

Treewidth and Dynamic Programming

TLDR
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

TLDR
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

TLDR
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.
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References

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On treewidth approximations

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TLDR
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

TLDR
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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TLDR
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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TLDR
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TLDR
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