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Enumerating Constrained Non-crossing Minimally Rigid Frameworks

David Avis·Naoki Katoh·Makoto Ohsaki·Ileana Streinu·Shin-ichi Tanigawa
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Abstract

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.

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David Avis, Naoki Katoh, Makoto Ohsaki, Ileana Streinu, Shin-ichi Tanigawa. 2006-11-07. Enumerating Constrained Non-crossing Minimally Rigid Frameworks. https://arxiv.org/abs/math/0608102

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