Homogeneity vs. adjacency: generalising some graph decomposition algorithms

Authors:
B. M. Bui Xuan;M. Habib;V. Limouzy;F. de Montgolfier
Affiliations:
LIRMM, Université Montpellier 2, France;LIAFA, Université Paris 7, France;LIAFA, Université Paris 7, France;LIAFA, Université Paris 7, France
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

Citing 10
Cited 1

Three partition refinement algorithms

SIAM Journal on Computing
Theory of 2-structures. Part I: clans, basic subclasses, and morphisms

Theoretical Computer Science
Modular decomposition and transitive orientation

Discrete Mathematics - Special issue on partial ordered sets
Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition

Journal of Algorithms
Efficient and practical algorithms for sequential modular decomposition

Journal of Algorithms
A New Linear Algorithm for Modular Decomposition

CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Efficient algorithms for testing the twins property

Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
The complexity of modular decomposition of Boolean functions

Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Linear-time modular decomposition of directed graphs

Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Revisiting t. uno and m. yagiura's algorithm

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

Unifying two graph decompositions with modular decomposition

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs and of 2-structures, but also decomposition by star cutsets.