A fully dynamic algorithm for modular decomposition and recognition of cographs

Ron Shamir, Roded Sharan*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

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.

Original languageEnglish
Pages (from-to)329-340
Number of pages12
JournalDiscrete Applied Mathematics
Volume136
Issue number2-3
DOIs
StatePublished - 15 Feb 2004
Event1st Cologne-Twente Workshop on Graphs and Combinatorial (CTW 2001) - Enschede, Netherlands
Duration: 6 Jun 20018 Jun 2001

Keywords

  • Cograph
  • Fully dynamic algorithm
  • Modular decomposition
  • Recognition

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