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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    AU - Langerman, Stefan

    AU - Meijer, Henk

    AU - O'Rourke, Joseph

    AU - Overmars, Mark

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