Enumerating Constrained Non-crossing Minimally Rigid Frameworks

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained non-crossing Laman frameworks) on a given generic set of $n$ points. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in $O(n^4)$ time and O(n) space, or, slightly different implementation, in $O(n^3)$ time and $O(n^2)$ space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is connected by flips which restore the Laman property.
14 pages, 3 figures

Keywords

Combinatorics, 68W01

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/115280

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608102
 http://arxiv.org/abs/math/0608102

Collections

arXiv