# Parameterized Algorithms for Modular-Width

@article{Gajarsk2013ParameterizedAF, title={Parameterized Algorithms for Modular-Width}, author={Jakub Gajarsk{\'y} and Michael Lampis and Sebastian Ordyniak}, journal={ArXiv}, year={2013}, volume={abs/1308.2858} }

It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty.
The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILPs…

## 69 Citations

Modular-Width: An Auxiliary Parameter for Parameterized Parallel Complexity

- MathematicsFAW
- 2017

Modular-width in parameterized parallel complexity is studied and it is shown that the weighted maximum clique problem and the maximum matching problem are fixed-parameter parallel-tractable (FPPT) when parameterized by this parameter.

Between Treewidth and Clique-Width

- Computer ScienceAlgorithmica
- 2015

The graph parameter sm-width is considered which lies between treewidth and clique-width and it is shown that MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set are all FPT parameterized by sm- width.

Solving Hamiltonian Cycle by an EPT Algorithm for a Non-sparse Parameter

- Computer ScienceCALDAM
- 2015

Saether and Telle address the problem of hard graph problems, such as Hamiltonian Cycle, by introducing a new parameter, split-matching-width, which lies between treewidth and clique-width in terms of generality, and show that even though graphs of restricted split-matched-width might be dense, solving problems such asHamiltonian Cycle can be done in FPT time.

Solving Hamiltonian Cycle by an EPT algorithm for a non-sparse parameter

- Computer ScienceDiscret. Appl. Math.
- 2017

Between Treewidth and Clique-Width

- Computer ScienceWG
- 2014

This paper seeks a structural graph parameter that shares some of the generality of clique-width without paying this price.

Co-Degeneracy and Co-Treewidth: Using the Complement to Solve Dense Instances

- Computer ScienceMFCS
- 2021

Evidence is given that co-treewidth is a useful width parameter for handling dense instances of problems for which an FPT algorithm for clique-width is unlikely to exist and an algorithmic framework for co-degeneracy is developed based on the notion of Bondy-Chvátal closure.

P-FPT algorithms for bounded clique-width graphs

- Computer Science, Mathematics
- 2019

This paper studies several graph theoretic problems for which hardness results exist and gives hardness results and P-FPT algorithms, using clique-width and some of its upper bounds as parameters, based on preprocessing methods using modular decomposition and split decomposition.

Polynomial Turing Compressions for Some Graph Problems Parameterized by Modular-Width

- Computer Science, MathematicsArXiv
- 2022

A recipe is developed that is able to simplify the process of obtaining polynomial Turing compressions for a class of graph problems parameterized by modular-width and new parameterized algorithms for these problems are obtained.

Parametrised Algorithms for Directed Modular Width

- Mathematics, Computer ScienceCALDAM
- 2020

Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width,…

Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width Graphs

- Computer Science, MathematicsACM Trans. Algorithms
- 2019

This article studies several graph-theoretic problems for which hardness results exist and gives hardness results and P-FPT algorithms, using clique-width and some of its upper bounds as parameters, based on preprocessing methods using modular decomposition and split decomposition.

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