Global Information Lookup Global Information

Modular decomposition information


In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can be a proper subset of another. Modules therefore lead to a recursive (hierarchical) decomposition of the graph, instead of just a partition.

There are variants of modular decomposition for undirected graphs and directed graphs. For each undirected graph, this decomposition is unique.

This notion can be generalized to other structures (for example directed graphs) and is useful to design efficient algorithms for the recognition of some graph classes, for finding transitive orientations of comparability graphs, for optimization problems on graphs, and for graph drawing.

and 23 Related for: Modular decomposition information

Request time (Page generated in 0.8285 seconds.)

Modular decomposition

Last Update:

In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected...

Word Count : 3177

Modular programming

Last Update:

by decomposition into smaller pieces, and all originating around the 1960s. While the historical usage of these terms has been inconsistent, "modular programming"...

Word Count : 1610

Power graph analysis

Last Update:

Modular decomposition can be used to compute a power graph by using the strong modules of the modular decomposition. Modules in modular decomposition...

Word Count : 1580

Module

Last Update:

module or modular in Wiktionary, the free dictionary. Module, modular and modularity may refer to the concept of modularity. They may also refer to: Modular design...

Word Count : 466

Modularity

Last Update:

Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety...

Word Count : 5314

Strongly connected component

Last Update:

consistently. Clique (graph theory) Connected component (graph theory) Modular decomposition Weak component Nuutila, Esko; Soisalon-Soininen, Eljas (1994), "On...

Word Count : 1639

Permutation graph

Last Update:

(up to permutation symmetry) if it is prime with respect to the modular decomposition. If ρ = ( σ 1 , σ 2 , . . . , σ n ) {\displaystyle \rho =(\sigma...

Word Count : 938

Modular design

Last Update:

Modular design, or modularity in design, is a design principle that subdivides a system into smaller parts called modules (such as modular process skids)...

Word Count : 2428

Glossary of graph theory

Last Update:

to shortest paths between all pairs of the triple. 2.  Modular decomposition, a decomposition of a graph into subgraphs within which all vertices connect...

Word Count : 15667

Functional decomposition

Last Update:

inference, hierarchical clustering, and quadtree decomposition are all examples of function decomposition. Many statistical inference methods can be thought...

Word Count : 1646

Decomposition matrix

Last Update:

In mathematics, and in particular modular representation theory, a decomposition matrix is a matrix that results from writing the irreducible ordinary...

Word Count : 115

Modular representation theory

Last Update:

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups...

Word Count : 2611

Strong perfect graph theorem

Last Update:

strong perfect graph theorem. A homogeneous pair is related to a modular decomposition of a graph. It is a partition of the graph into three subsets V1...

Word Count : 1769

Pyrolysis

Last Update:

Pyrolysis is the process of thermal decomposition of materials at elevated temperatures, often in an inert atmosphere. The word pyrolysis is coined from...

Word Count : 8121

Integer factorization

Last Update:

in computer science) In number theory, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer...

Word Count : 2981

Modularity of mind

Last Update:

Modularity of mind is the notion that a mind may, at least in part, be composed of innate neural structures or mental modules which have distinct, established...

Word Count : 3035

Cograph

Last Update:

cotree representation constructed, using modular decomposition, partition refinement, LexBFS , or split decomposition. Once a cotree representation has been...

Word Count : 2717

Monstrous moonshine

Last Update:

shortened by replacing the usual triangular decomposition of the Monster Lie algebra with a decomposition into a sum of gl2 and two free Lie algebras...

Word Count : 4478

Pebble bed modular reactor

Last Update:

methanol); and to produce hydrogen and oxygen by decomposing water thermochemically. The PBMR is modular in that only small to mid-sized units will be designed...

Word Count : 1386

Water splitting

Last Update:

radiation has not been commercialized. Electrolysis of water is the decomposition of water (H2O) into oxygen (O2) and hydrogen (H2): Production of hydrogen...

Word Count : 1855

Fourier transform on finite groups

Last Update:

theorem it decomposes as a direct product of matrix rings. The Fourier transform on finite groups explicitly exhibits this decomposition, with a matrix...

Word Count : 1845

Semisimple representation

Last Update:

complementary representation). The decomposition of a semisimple representation into simple ones, called a semisimple decomposition, need not be unique; for example...

Word Count : 3849

Nervous system network models

Last Update:

model may indeed be analyzed at this top level of modular decomposition, we need to further decompose basal ganglia, BG, as shown in Figure 3(c) if we...

Word Count : 5049

PDF Search Engine © AllGlobal.net