Three partition refinement algorithms
SIAM Journal on Computing
Incremental modular decomposition
Journal of the ACM (JACM)
Primitivity is hereditary for 2-structures
Theoretical Computer Science
Recognizing P4-sparse graphs in linear time
SIAM Journal on Computing
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Efficient parallel recognition algorithms of cographs and distance hereditary graphs
Discrete Applied Mathematics
P-Components and the Homogeneous Decomposition of Graphs
SIAM Journal on Discrete Mathematics
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Discrete Mathematics
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
Restricted permutations and the wreath product
Discrete Mathematics
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
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
Graph decompositions and factorizing permutations
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
A fully dynamic algorithm for modular decomposition and recognition of cographs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs
Discrete Applied Mathematics
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Fully dynamic recognition algorithm and certificate for directed cograph
Discrete Applied Mathematics
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A more efficient algorithm for perfect sorting by reversals
Information Processing Letters
Minimal proper interval completions
Information Processing Letters
Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs
SIAM Journal on Discrete Mathematics
Longest Common Separable Pattern Among Permutations
CPM '07 Proceedings of the 18th annual symposium on Combinatorial Pattern Matching
Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A Simple Linear Time LexBFS Cograph Recognition Algorithm
SIAM Journal on Discrete Mathematics
Applying Modular Decomposition to Parameterized Cluster Editing Problems
Theory of Computing Systems
Algorithmic aspects of a general modular decomposition theory
Discrete Applied Mathematics
Fully Dynamic Representations of Interval Graphs
Graph-Theoretic Concepts in Computer Science
A simple linear time algorithm for cograph recognition
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
The computational complexity of the role assignment problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
An improved fixed-parameter algorithm for minimum-flip consensus trees
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Improved algorithms for bicluster editing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A representation theorem for union-difference families and application
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Common Intervals of Multiple Permutations
Algorithmica
Tree-representation of set families and applications to combinatorial decompositions
European Journal of Combinatorics
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Algorithms for some h-join decompositions
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Complexity and parameterized algorithms for Cograph Editing
Theoretical Computer Science
Speeding up graph clustering via modular decomposition based compression
Proceedings of the 28th Annual ACM Symposium on Applied Computing
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Polynomial kernels for Proper Interval Completion and related problems
Information and Computation
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
(Nearly-)tight bounds on the contiguity and linearity of cographs
Theoretical Computer Science
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Modular decomposition is a technique that applies to (but is not restricted to) graphs. The notion of a module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 1970's, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research.