Document Type
Article
Publication Date
1-1-1999
Publication Title
Proceedings of the Annual Symposium on Computational Geometry
Abstract
We present advances on the open problem of characterizing vertex-edge visibility graphs (ve-graphs), reduced by results of O'Rourke and Streinu to a stretchability question for pseudo-polygons. We introduce star-like pseudo-polygons as a special subclass containing all the known instances of non-stretchable pseudo-polygons. We give a complete combinatorial characterization and a linear-time decision procedure for star-like pseudo-polygon stretchability and star-like ve-graph recognition. To the best of our knowledge, this is the first problem in computational geometry for which a combinatorial characterization was found by first isolating the oriented matroid substructure and then separately solving the stretchability question. It is also the first class (as opposed to isolated examples) of oriented matroids for which an efficient stretchability decision procedure based on combinatorial criteria is given. The difficulty of the general stretchability problem implied by Mnev's Universality Theorem makes this a result of independent interest in the theory of oriented matroids.
First Page
274
Last Page
280
DOI
10.1145/304893.304980
Recommended Citation
Streinu, Ileana, "Stretchability of Star-Like Pseudo-Visibility Graphs" (1999). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/267
Comments
Archived as published.