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Inductive constructions for combinatorial local and global rigidity

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review

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Standard

Inductive constructions for combinatorial local and global rigidity. / Nixon, Anthony Keith; Ross, Elissa.
Handbook of Geometric Constraint Systems Principles. ed. / Meera Sitharam; Audrey St. John; Jessica Sidman. CRC Press, 2018. (Discrete Mathematics and Its Applications).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review

Harvard

Nixon, AK & Ross, E 2018, Inductive constructions for combinatorial local and global rigidity. in M Sitharam, A St. John & J Sidman (eds), Handbook of Geometric Constraint Systems Principles. Discrete Mathematics and Its Applications, CRC Press. https://doi.org/10.1201/9781315121116

APA

Nixon, A. K., & Ross, E. (2018). Inductive constructions for combinatorial local and global rigidity. In M. Sitharam, A. St. John, & J. Sidman (Eds.), Handbook of Geometric Constraint Systems Principles (Discrete Mathematics and Its Applications). CRC Press. https://doi.org/10.1201/9781315121116

Vancouver

Nixon AK, Ross E. Inductive constructions for combinatorial local and global rigidity. In Sitharam M, St. John A, Sidman J, editors, Handbook of Geometric Constraint Systems Principles. CRC Press. 2018. (Discrete Mathematics and Its Applications). doi: 10.1201/9781315121116

Author

Nixon, Anthony Keith ; Ross, Elissa. / Inductive constructions for combinatorial local and global rigidity. Handbook of Geometric Constraint Systems Principles. editor / Meera Sitharam ; Audrey St. John ; Jessica Sidman. CRC Press, 2018. (Discrete Mathematics and Its Applications).

Bibtex

@inbook{e52788d47c924a0c8628f9cd5256ee3d,
title = "Inductive constructions for combinatorial local and global rigidity",
abstract = "Determining the rigidity, or global rigidity, of a given framework is NP-hard. This chapter considers a variety of local operations on graphs and when they are known to preserve the rigidity or global rigidity of frameworks. However, the situation improves for generic frameworks where one can linearize the problem and characterize generic rigidity via the rank of the rigidity matrix. A key topic in rigidity theory, perhaps the fundamental topic, is to characterize generic rigidity, and generic global rigidity, in purely combinatorial terms. For body-bar frameworks, rigidity can be elegantly characterized via tree packing in arbitrary dimension. Known characterizations of incidental rigidity are limited to very small groups but make significant use of inductive constructions. It is helpful to have inductive methods to generate families of globally rigid direction-length graphs, and this provides a tool to verify the global rigidity of certain frameworks.",
author = "Nixon, {Anthony Keith} and Elissa Ross",
year = "2018",
month = jul,
day = "20",
doi = "10.1201/9781315121116",
language = "English",
isbn = "9781498738910",
series = "Discrete Mathematics and Its Applications",
publisher = "CRC Press",
editor = "Sitharam, {Meera } and {St. John}, Audrey and Jessica Sidman",
booktitle = "Handbook of Geometric Constraint Systems Principles",

}

RIS

TY - CHAP

T1 - Inductive constructions for combinatorial local and global rigidity

AU - Nixon, Anthony Keith

AU - Ross, Elissa

PY - 2018/7/20

Y1 - 2018/7/20

N2 - Determining the rigidity, or global rigidity, of a given framework is NP-hard. This chapter considers a variety of local operations on graphs and when they are known to preserve the rigidity or global rigidity of frameworks. However, the situation improves for generic frameworks where one can linearize the problem and characterize generic rigidity via the rank of the rigidity matrix. A key topic in rigidity theory, perhaps the fundamental topic, is to characterize generic rigidity, and generic global rigidity, in purely combinatorial terms. For body-bar frameworks, rigidity can be elegantly characterized via tree packing in arbitrary dimension. Known characterizations of incidental rigidity are limited to very small groups but make significant use of inductive constructions. It is helpful to have inductive methods to generate families of globally rigid direction-length graphs, and this provides a tool to verify the global rigidity of certain frameworks.

AB - Determining the rigidity, or global rigidity, of a given framework is NP-hard. This chapter considers a variety of local operations on graphs and when they are known to preserve the rigidity or global rigidity of frameworks. However, the situation improves for generic frameworks where one can linearize the problem and characterize generic rigidity via the rank of the rigidity matrix. A key topic in rigidity theory, perhaps the fundamental topic, is to characterize generic rigidity, and generic global rigidity, in purely combinatorial terms. For body-bar frameworks, rigidity can be elegantly characterized via tree packing in arbitrary dimension. Known characterizations of incidental rigidity are limited to very small groups but make significant use of inductive constructions. It is helpful to have inductive methods to generate families of globally rigid direction-length graphs, and this provides a tool to verify the global rigidity of certain frameworks.

U2 - 10.1201/9781315121116

DO - 10.1201/9781315121116

M3 - Chapter (peer-reviewed)

SN - 9781498738910

T3 - Discrete Mathematics and Its Applications

BT - Handbook of Geometric Constraint Systems Principles

A2 - Sitharam, Meera

A2 - St. John, Audrey

A2 - Sidman, Jessica

PB - CRC Press

ER -