author: | Ross M. McConnell and Jeremy P. Spinrad |
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title: | Ordered Vertex Partitioning |
keywords: | Modular Decomposition, Substitution Decomposition, Transitive Orientation |
abstract: | 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.
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reference: | Ross M. McConnell and Jeremy P. Spinrad (2000), Ordered Vertex Partitioning, Discrete Mathematics and Theoretical Computer Science 4, pp. 45-60 |
bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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pdf-source: | dm040104.pdf (200 K) |
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