A fully dynamic algorithm for modular decomposition and recognition of cographs

The problem of dynamically recognizing a graph property calls for efficiently deciding if an input graph satisfies the property under repeated modifications to its set of vertices and edges. The input to the problem consists of a series of modifications to be performed on the graph. The objective is...

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Published in:Discrete Applied Mathematics Vol. 136; no. 2; pp. 329 - 340
Main Authors: Shamir, Ron, Sharan, Roded
Format: Journal Article Conference Proceeding
Language:English
Published: Lausanne Elsevier B.V 15.02.2004
Amsterdam Elsevier
New York, NY
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Cograph
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Fully dynamic algorithm
Graph theory
Mathematics
Modular decomposition
Recognition
Sciences and techniques of general use
Theoretical computing
Modular decomposition
Fully dynamic algorithm
Cograph
Recognition
Graph decomposition
Tree(graph)
Computer theory
Decomposition method
Edge set
Optimization
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Abstract The problem of dynamically recognizing a graph property calls for efficiently deciding if an input graph satisfies the property under repeated modifications to its set of vertices and edges. The input to the problem consists of a series of modifications to be performed on the graph. The objective is to maintain a representation of the graph as long as the property holds, and to detect when it ceases to hold. In this paper, we solve the dynamic recognition problem for the class of cographs and some of its subclasses. Our approach is based on maintaining the modular decomposition tree of the dynamic graph, and using this tree for the recognition. We give the first fully dynamic algorithm for maintaining the modular decomposition tree of a cograph. We thereby obtain fully dynamic algorithms for the recognition of cographs, threshold graphs, and trivially perfect graphs. All these algorithms work in constant time per edge modification and O( d) time per d-degree vertex modification.
AbstractList The problem of dynamically recognizing a graph property calls for efficiently deciding if an input graph satisfies the property under repeated modifications to its set of vertices and edges. The input to the problem consists of a series of modifications to be performed on the graph. The objective is to maintain a representation of the graph as long as the property holds, and to detect when it ceases to hold. In this paper, we solve the dynamic recognition problem for the class of cographs and some of its subclasses. Our approach is based on maintaining the modular decomposition tree of the dynamic graph, and using this tree for the recognition. We give the first fully dynamic algorithm for maintaining the modular decomposition tree of a cograph. We thereby obtain fully dynamic algorithms for the recognition of cographs, threshold graphs, and trivially perfect graphs. All these algorithms work in constant time per edge modification and O( d) time per d-degree vertex modification.
Author Sharan, Roded
Shamir, Ron
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Cites_doi 10.1016/0012-365X(78)90178-4
10.1137/S0097539700372216
10.1145/58562.59300
10.1137/1.9780898719796
10.1137/S0097539792269095
10.1007/3-540-61576-8_70
10.1007/BFb0017474
10.1137/0214065
10.1016/0166-218X(81)90013-5
10.1007/BF02579333
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Issue 2
Keywords Modular decomposition
Fully dynamic algorithm
Cograph
Recognition
Graph decomposition
Tree(graph)
Computer theory
Decomposition method
Edge set
Optimization
Language English
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SubjectTerms Algorithmics. Computability. Computer arithmetics
Applied sciences
Cograph
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Fully dynamic algorithm
Graph theory
Mathematics
Modular decomposition
Recognition
Sciences and techniques of general use
Theoretical computing
Title A fully dynamic algorithm for modular decomposition and recognition of cographs
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