Enumerating Constrained Non-crossing Minimally Rigid Frameworks

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...

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Veröffentlicht in:Discrete & computational geometry 2008-07, Vol.40 (1), p.31-46
Hauptverfasser: Avis, David, Katoh, Naoki, Ohsaki, Makoto, Streinu, Ileana, Tanigawa, Shin-ichi
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Sprache:eng
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Zusammenfassung: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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-007-9026-x