Strongly rigid tensegrity graphs on the line

Bill Jackson, T. Jordán, Csaba Király

Research output: Contribution to journalArticle

Abstract

Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.

Original languageEnglish
Pages (from-to)1147-1149
Number of pages3
JournalDiscrete Applied Mathematics
Volume161
Issue number7-8
DOIs
Publication statusPublished - May 2013

Fingerprint

Tensegrity
Struts
Cables
Line
Graph in graph theory
Cable
Set of points
NP-complete problem
Lower bound
Framework

Keywords

  • Graph
  • NP-hard
  • Rigidity
  • Tensegrity framework

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Strongly rigid tensegrity graphs on the line. / Jackson, Bill; Jordán, T.; Király, Csaba.

In: Discrete Applied Mathematics, Vol. 161, No. 7-8, 05.2013, p. 1147-1149.

Research output: Contribution to journalArticle

Jackson, Bill ; Jordán, T. ; Király, Csaba. / Strongly rigid tensegrity graphs on the line. In: Discrete Applied Mathematics. 2013 ; Vol. 161, No. 7-8. pp. 1147-1149.
@article{ec45dca86bea42ea9c8fa9a6be4b444c,
title = "Strongly rigid tensegrity graphs on the line",
abstract = "Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.",
keywords = "Graph, NP-hard, Rigidity, Tensegrity framework",
author = "Bill Jackson and T. Jord{\'a}n and Csaba Kir{\'a}ly",
year = "2013",
month = "5",
doi = "10.1016/j.dam.2012.12.009",
language = "English",
volume = "161",
pages = "1147--1149",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "7-8",

}

TY - JOUR

T1 - Strongly rigid tensegrity graphs on the line

AU - Jackson, Bill

AU - Jordán, T.

AU - Király, Csaba

PY - 2013/5

Y1 - 2013/5

N2 - Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.

AB - Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.

KW - Graph

KW - NP-hard

KW - Rigidity

KW - Tensegrity framework

UR - http://www.scopus.com/inward/record.url?scp=84875225027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875225027&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.12.009

DO - 10.1016/j.dam.2012.12.009

M3 - Article

AN - SCOPUS:84875225027

VL - 161

SP - 1147

EP - 1149

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 7-8

ER -