Discrete Mathematics & Theoretical Computer Science
| author: | Selma Djelloul and Mekkia Kouider |
|---|---|
| title: | Minimum survivable graphs with bounded distance increase |
| keywords: | distance, fault-tolerance, spanning subgraph |
| abstract: | We study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is
a non-negative integer, if after the
removal of any vertex no distance in the surviving
graph increases by more than k.
In the design of interconnection networks such
graphs guarantee good fault-tolerance properties.
We give upper and lower bounds on the minimum
number of edges of a k-self-repairing graph for
prescribed k and n, where n is the order of
the graph. We prove that the problem of finding,
in a k-self-repairing graph, a spanning
k-self-repairing subgraph of minimum size
is NP-Hard.
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: | Selma Djelloul and Mekkia Kouider (2003), Minimum survivable graphs with bounded distance increase, Discrete Mathematics and Theoretical Computer Science 6, pp. 123-132 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dm060110.ps.gz (45 K) |
| ps-source: | dm060110.ps (150 K) |
| pdf-source: | dm060110.pdf (108 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.