A note on reconfiguring tree linkages: Trees can lock

Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides

Research output: Contribution to journalArticle

Abstract

It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2(Ω(N)) equivalence classes of configurations.

Original languageEnglish (US)
Pages (from-to)293-297
Number of pages5
JournalDiscrete Applied Mathematics
Volume117
Issue number1-3
DOIs
StatePublished - Mar 15 2002

Fingerprint

Equivalence classes
Linkage
Configuration
Equivalence class
Straight Line
Polygon
Motion

Keywords

  • Distance geometry
  • Graph embedding
  • Linkage reconfiguration
  • Motion planning
  • Tree embedding

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Biedl, T., Demaine, E., Demaine, M., Lazard, S., Lubiw, A., O'Rourke, J., ... Whitesides, S. (2002). A note on reconfiguring tree linkages: Trees can lock. Discrete Applied Mathematics, 117(1-3), 293-297. https://doi.org/10.1016/S0166-218X(01)00229-3

A note on reconfiguring tree linkages : Trees can lock. / Biedl, Therese; Demaine, Erik; Demaine, Martin; Lazard, Sylvain; Lubiw, Anna; O'Rourke, Joseph; Robbins, Steve; Streinu, Ileana; Toussaint, Godfried; Whitesides, Sue.

In: Discrete Applied Mathematics, Vol. 117, No. 1-3, 15.03.2002, p. 293-297.

Research output: Contribution to journalArticle

Biedl, T, Demaine, E, Demaine, M, Lazard, S, Lubiw, A, O'Rourke, J, Robbins, S, Streinu, I, Toussaint, G & Whitesides, S 2002, 'A note on reconfiguring tree linkages: Trees can lock', Discrete Applied Mathematics, vol. 117, no. 1-3, pp. 293-297. https://doi.org/10.1016/S0166-218X(01)00229-3
Biedl T, Demaine E, Demaine M, Lazard S, Lubiw A, O'Rourke J et al. A note on reconfiguring tree linkages: Trees can lock. Discrete Applied Mathematics. 2002 Mar 15;117(1-3):293-297. https://doi.org/10.1016/S0166-218X(01)00229-3
Biedl, Therese ; Demaine, Erik ; Demaine, Martin ; Lazard, Sylvain ; Lubiw, Anna ; O'Rourke, Joseph ; Robbins, Steve ; Streinu, Ileana ; Toussaint, Godfried ; Whitesides, Sue. / A note on reconfiguring tree linkages : Trees can lock. In: Discrete Applied Mathematics. 2002 ; Vol. 117, No. 1-3. pp. 293-297.
@article{61e1159682d54be7bbb52551079526e7,
title = "A note on reconfiguring tree linkages: Trees can lock",
abstract = "It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2(Ω(N)) equivalence classes of configurations.",
keywords = "Distance geometry, Graph embedding, Linkage reconfiguration, Motion planning, Tree embedding",
author = "Therese Biedl and Erik Demaine and Martin Demaine and Sylvain Lazard and Anna Lubiw and Joseph O'Rourke and Steve Robbins and Ileana Streinu and Godfried Toussaint and Sue Whitesides",
year = "2002",
month = "3",
day = "15",
doi = "10.1016/S0166-218X(01)00229-3",
language = "English (US)",
volume = "117",
pages = "293--297",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - A note on reconfiguring tree linkages

T2 - Trees can lock

AU - Biedl, Therese

AU - Demaine, Erik

AU - Demaine, Martin

AU - Lazard, Sylvain

AU - Lubiw, Anna

AU - O'Rourke, Joseph

AU - Robbins, Steve

AU - Streinu, Ileana

AU - Toussaint, Godfried

AU - Whitesides, Sue

PY - 2002/3/15

Y1 - 2002/3/15

N2 - It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2(Ω(N)) equivalence classes of configurations.

AB - It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2(Ω(N)) equivalence classes of configurations.

KW - Distance geometry

KW - Graph embedding

KW - Linkage reconfiguration

KW - Motion planning

KW - Tree embedding

UR - http://www.scopus.com/inward/record.url?scp=84867972776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867972776&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(01)00229-3

DO - 10.1016/S0166-218X(01)00229-3

M3 - Article

AN - SCOPUS:84867972776

VL - 117

SP - 293

EP - 297

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -