Flat-state connectivity of linkages under dihedral motions

Greg Aloupis, Erik D. Demaine, Vida Dujmović, Jeff Erickson, Stefan Langerman, Henk Meijer, Joseph O'Rourke, Mark Overmars, Michael Soss, Ileana Streinu, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We explore which classes of linkages have the property that each pair of their flat states - that is, their embeddings in ℝ2 without self-intersection - can be connected by a continuous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein models. Our positive results include proofs that open chains with nonacute angles are flat-state connected, as are closed orthogonal unit-length chains. Among our negative results is an example of an orthogonal graph linkage that is flat-state disconnected. Several additional results are obtained for other restrictedclasses of linkages. Many open problems are posed.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings
Pages369-380
Number of pages12
DOIs
StatePublished - Dec 1 2002
Event13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada
Duration: Nov 21 2002Nov 23 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2518 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th Annual International Symposium on Algorithms and Computation, ISAAC 2002
CountryCanada
CityVancouver, BC
Period11/21/0211/23/02

Fingerprint

Linkage
Connectivity
Self-intersection
Motion
Chain length
Angle
Proteins
Open Problems
Protein
Closed
Unit
Graph in graph theory
Model
Class

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Aloupis, G., Demaine, E. D., Dujmović, V., Erickson, J., Langerman, S., Meijer, H., ... Toussaint, G. (2002). Flat-state connectivity of linkages under dihedral motions. In Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings (pp. 369-380). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_33

Flat-state connectivity of linkages under dihedral motions. / Aloupis, Greg; Demaine, Erik D.; Dujmović, Vida; Erickson, Jeff; Langerman, Stefan; Meijer, Henk; O'Rourke, Joseph; Overmars, Mark; Soss, Michael; Streinu, Ileana; Toussaint, Godfried.

Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings. 2002. p. 369-380 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Aloupis, G, Demaine, ED, Dujmović, V, Erickson, J, Langerman, S, Meijer, H, O'Rourke, J, Overmars, M, Soss, M, Streinu, I & Toussaint, G 2002, Flat-state connectivity of linkages under dihedral motions. in Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2518 LNCS, pp. 369-380, 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, Vancouver, BC, Canada, 11/21/02. https://doi.org/10.1007/3-540-36136-7_33
Aloupis G, Demaine ED, Dujmović V, Erickson J, Langerman S, Meijer H et al. Flat-state connectivity of linkages under dihedral motions. In Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings. 2002. p. 369-380. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-36136-7_33
Aloupis, Greg ; Demaine, Erik D. ; Dujmović, Vida ; Erickson, Jeff ; Langerman, Stefan ; Meijer, Henk ; O'Rourke, Joseph ; Overmars, Mark ; Soss, Michael ; Streinu, Ileana ; Toussaint, Godfried. / Flat-state connectivity of linkages under dihedral motions. Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings. 2002. pp. 369-380 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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