Discrete Mathematics & Theoretical Computer Science
| author: | Ross M. McConnell and Jeremy P. Spinrad |
|---|---|
| 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(n2).
The best known time bounds for the problems are O(n+m) but they
involve sophisticated techniques.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |
| 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. |
| ps.gz-source: | dm040104.ps.gz (47 K) |
| ps-source: | dm040104.ps (155 K) |
| pdf-source: | dm040104.pdf (200 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.