# Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization

@inproceedings{Bodlaender2011PreprocessingFT, title={Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization}, author={Hans L. Bodlaender and Bart M. P. Jansen and Stefan Kratsch}, booktitle={SIAM Journal on Discrete Mathematics}, year={2011} }

The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first apply an array of preprocessing rules that simplify and shrink it. This work seeks to prove rigorous performance guarantees for such preprocessing rules---known rules as well as more recent ones---by studying them in the framework of kernelization from…

## 64 Citations

### Kernelization, Preprocessing for Treewidth

- Computer ScienceEncyclopedia of Algorithms
- 2016

This work undertakes a theoretical study of preprocessing for the NP-hard TREEWIDTH problem of finding a tree decomposition of width at most k for a given graph G, and studies upper and lower bounds within the framework of kernelization from parameterized complexity.

### Kernel Bounds for Structural Parameterizations of Pathwidth

- Mathematics, Computer ScienceSWAT
- 2012

The main result is that, unless NP ⊆ coNP/poly, Pathwidth admits no polynomial kernelization even when parameterized by the vertex deletion distance to a clique, by giving a cross-composition from Cutwidth.

### The Power of Data Reduction : Kernels for Fundamental Graph Problems

- Computer Science, Mathematics
- 2013

The concept of kernelization, developed within the field of parameterized complexity theory, is used to give a mathematical analysis of the power of data reduction for dealing with fundamental NP-hard graph problems and it is proved that Treewidth and Pathwidth do not admit polynomial kernels parameterized by the vertex-deletion distance to a clique, unless thePolynomial hierarchy collapses.

### Kernelization Rules for Special Treewidth and Spaghetti Treewidth

- Computer Science, Mathematics
- 2012

It is shown that Special Treewidth has a kernel with O(`) vertices, where ` denotes the size of a vertex cover, which implies that given an instance (G, k) of SpecialTreewidth the authors can efficiently reduce its size to O((`∗)3) verticing.

### FPT is characterized by useful obstruction sets: Connecting algorithms, kernels, and quasi-orders

- Computer Science, MathematicsTOCT
- 2014

This work shows how exponential-size minor-minimal obstructions for pathwidth k form the crucial ingredient in a novel or-cross-compositions for k-Pathwidth, complementing the trivial and-composition that is known for this problem.

### Kernelization Rules for Special Treewidth and Spaghetti Treewidth

- Computer Science, Mathematics
- 2012

It is shown that Special Treewidth has a kernel with O ( ( cid:96) 3 ) vertices, where (cid: 96) denotes the size of a vertex cover, which implies that given an instance ( G, k) of SpecialTreewidth the authors can eﬃciently reduce its size to O (( (cide:96):96) ∗ ) 3) vertices.

### Representative Sets and Irrelevant Vertices: New Tools for Kernelization

- Computer Science, Mathematics2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

This work applies the representative sets tool to the problem of finding irrelevant vertices in graph cut problems, that is, vertices which can be made undeletable without affecting the status of the problem, and gives the first significant progress towards a polynomial kernel for the Multiway Cut problem.

### Kernelization of packing problems

- Computer Science, MathematicsSODA
- 2012

This work shows lower bounds for the kernelization of d-Set Matching and other packing problems, and applies this scheme to the vertex cover problem, which allows us to replace the number-theoretical construction by Dell and Van Melkebeek with shorter elementary arguments.

### Recent developments in kernelization: A survey

- Computer ScienceBull. EATCS
- 2014

This survey gives a general introduction to the area of kernelization and discusses some recent developments, and attempts a reasonably self-contained update and introduction on the following topics: Lower bounds for kernelization, taking into account the recent progress on the and-conjecture.

### On Polynomial Kernels for Structural Parameterizations of Odd Cycle Transversal

- MathematicsIPEC
- 2011

The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite (i.e., 2-colorable) by deleting at most l vertices. We study structural parameterizations of OCT with respect…

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