Analyzing Rigidity with Pebble Games

Audrey Lee, University of Massachusetts Amherst
Ileana Streinu, Smith College
Louis Theran, University of Massachusetts Amherst

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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.