Discrete Mathematics & Theoretical Computer Science
Volume 3 n° 1 (1998), pp. 1-10
author: | Ulrik Brandes and Dagmar Handke |
---|---|
title: | NP-Completeness Results for Minimum Planar Spanners |
keywords: | graph spanners, NP-completeness, planar graphs |
abstract: | For any fixed parameter t greater or equal to 1, a t-spanner of a graph G is a spanning subgraph in which the distance between every pair of vertices is at most t times their distance in G. A minimum t-spanner is a t-spanner with minimum total edge weight or, in unweighted graphs, minimum number of edges. In this paper, we prove the NP-hardness of finding minimum t-spanners for planar weighted graphs and digraphs if t greater or equal to 3, and for planar unweighted graphs and digraphs if t greater or equal to 5. We thus extend results on that problem to the interesting case where the instances are known to be planar. We also introduce the related problem of finding minimum planar t-spanners and establish its NP-hardness for similar fixed values of t. |
reference: | Ulrik Brandes and Dagmar Handke (1998), NP-Completeness Results for Minimum Planar Spanners, Discrete Mathematics and Theoretical Computer Science 3, pp. 1-10 |
ps.gz-source: | dm030101.ps.gz |
ps-source: | dm030101.ps |
pdf-source: | dm030101.pdf |
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.
Automatically produced on Tue Jan 19 17:49:03 MET 1999 by gustedt