scholarly journals Modular decomposition and transitive orientation

1999 ◽  
Vol 201 (1-3) ◽  
pp. 189-241 ◽  
Author(s):  
Ross M. McConnell ◽  
Jeremy P. Spinrad
Keyword(s):  
Modular Decomposition ◽  
Transitive Orientation

scholarly journals Ordered Vertex Partitioning

2000 ◽  
Vol Vol. 4 no. 1 ◽  
Author(s):  
Ross M. Mcconnell ◽  
Jeremy P. Spinrad
Keyword(s):  
Canonical Representation ◽  
Modular Decomposition ◽  
Running Time ◽  
Dual Problems ◽  
International Audience ◽  
Transitive Orientation ◽  
Time Bounds

International audience A transitive orientation of a graph is an orientation of the edges that produces a transitive digraph. The modular decomposition of a graph is a canonical representation of all of its modules. Finding a transitive orientation and finding the modular decomposition are in some sense dual problems. In this paper, we describe a simple O(n + m \log n) algorithm that uses this duality to find both a transitive orientation and the modular decomposition. Though the running time is not optimal, this algorithm is much simpler than any previous algorithms that are not Ω (n^2). The best known time bounds for the problems are O(n+m) but they involve sophisticated techniques.

Modular Decomposition of Flow Chart Path Method and its Application

2011 ◽  
Vol 418-420 ◽  
pp. 2206-2210
Author(s):  
Meng Qi Li ◽  
Dong Ying Li
Keyword(s):  
Complex System ◽  
Case Analysis ◽  
Flow Chart ◽  
Function Model ◽  
Modular Decomposition ◽  
Dependency Relationship ◽  
Product Function ◽  
Paper Product ◽  
Material Information ◽  
Relationship Of

Modular decomposition is the key to simplify complex system. In this paper product function model is built based on flow chart description of energy, substance/material information. According to dependency relationship of function, function modularization is done respectively with module defining ways of main path method (MPM), branch path method (BPM) and conversion-conduction method (CCM). And modular decomposition of flow chart path method is established, concerned procedures and cautions during the implementing course are defined, and the purpose and effectiveness of modular decomposition of flow chart pass are confirmed through case analysis.

scholarly journals Decomposing Sets of Inversions

10.37236/2609 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Lukas Katthän
Keyword(s):  
Modular Decomposition ◽  
Substitution Decomposition ◽  
Special Case

In this paper we consider the question how the set of inversions of a permutation $\pi \in S_n$ can be partitioned into two subsets, which are themselves inversion sets of permutations in $S_n$. Our method is to study the modular decomposition of the inversion graph of $\pi$. A correspondence to the substitution decomposition of $\pi$ is also given. Moreover, we consider the special case of multiplicative decompositions.

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