Enumerating Constrained Non-crossing Minimally Rigid Frameworks |
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Authors: | David Avis Naoki Katoh Makoto Ohsaki Ileana Streinu Shin-ichi Tanigawa |
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Institution: | (1) School of Computer Science, McGill University, McGill, Canada;(2) Department of Architecture and Architectural Engineering, Kyoto University Katsura, Nishikyo-ku, Kyoto 615-8450, Japan;(3) Dept. of Comp. Science, Smith College, Northampton, MA 01063, USA |
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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, which we call constrained non-crossing Laman frameworks, on a given set of
n points in the plane. 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, with a 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 preserve the Laman property.
D. Avis’s research was supported by NSERC and FQRNT grants.
N. Katoh’s, M. Ohsaki’s and S.-i. Tanigawa’s research was supported by NEXT Grant-in-Aid for Scientific Research on priority
areas of New Horizons in Computing.
I. Streinu’s research was supported by NSF grant CCF-0430990 and NSF-DARPA CARGO CCR-0310661. |
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Keywords: | Geometric enumeration Rigidity Constrained non-crossing minimally rigid frameworks Constrained Delaunay triangulation |
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