Analyzing rigidity with pebble games

Authors:
Audrey Lee;Ileana Streinu;Louis Theran
Affiliations:
University of Massachusetts Amherst, Amherst, MA, USA;Smith College, Northampton, MA, USA;University of Massachusetts Amherst, Amherst, MA, USA
Venue:
Proceedings of the twenty-fourth annual symposium on Computational geometry
Year:
2008

Citing 2
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An algorithm for two-dimensional rigidity percolation: the pebble game

Journal of Computational Physics
Sparse hypergraphs and pebble game algorithms

European Journal of Combinatorics

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Abstract

How many pair-wise distances must be prescribed between an unknown set of points, and how should they be distributed, to determine only a discrete set of possible solutions? These questions, and related generalizations, are central in a variety of applications. Combinatorial rigidity shows that in two-dimensions one can get the answer, generically, via an efficiently testable sparse graph property. We present a video and a web site illustrating algorithmic results for a variety of rigidity-related problems, as well as abstract generalizations. Our accompanying interactive software is based on a comprehensive implementation of the pebble game paradigm.