Three partition refinement algorithms
SIAM Journal on Computing
Theory of 2-structures. Part I: clans, basic subclasses, and morphisms
Theoretical Computer Science
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Weighted parameters in (P5,&Pmacr;5)-free graphs
Discrete Applied Mathematics
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Directed Graphs by Clan-Based Decomposition
GD '95 Proceedings of the Symposium on Graph Drawing
Substitution Decomposition on Chordal Graphs and Applications
ISA '91 Proceedings of the 2nd International Symposium on 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)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Linear-time modular decomposition of directed graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
The complexity of modular decomposition of boolean functions
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs
SIAM Journal on Discrete Mathematics
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A generic approach to decomposition algorithms, with an application to digraph decomposition
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Survey: A survey of the algorithmic aspects of modular decomposition
Computer Science Review
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A new general decomposition theory inspired by modular graph decomposition is presented. This helps in unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, this new notion called homogeneous modules not only captures the classical graph modules but also allows handling 2-connected components, star-cutsets, and other vertex subsets. The main result is that most of the nice algorithmic tools developed for the modular decomposition of graphs still apply efficiently on our generalisation of modules. Besides, when an essential axiom is satisfied, almost all the important properties can be retrieved. For this case, an algorithm given by Ehrenfeucht, Gabow, McConnell and Sullivan [A. Ehrenfeucht, H. Gabow, R. McConnell, S. Sullivan, An O(n^2) Divide-and-Conquer Algorithm for the prime tree decomposition of two-structures and modular decomposition of graphs, Journal of Algorithms 16 (1994) 283-294.] is generalised and yields a very efficient solution to the associated decomposition problem.