lec11 - Geometric Constraints April 4, 6 & 11...

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Unformatted text preview: Geometric Constraints April 4, 6 & 11 Instructor: Dr.Meera Sitharam April 14, 2006 Objects in discussion Infinitesimal Rigidity Matroids. Generic Rigidity Matroids. Abstract Rigidity Matroids. Some Observations 1. Recall from previous lectures: Every greedy algorithm has an underly- ing matroid, and every matroid has a greedy algorithm on top of it 2. Just like looking at Independent sets in Matroids, we look for rigid sets in Abstract Rigidity Matroids 3. Rigidity is the same as Infinitesimal Rigidity for Generic embeddings 4. In order to define a Generic Rigidity Matroid we need an embedding, but this is not the case with Abstract Rigidity Matroids, Thus we are moving for a purely combinatorial characterization with ARMs 5. Class of Infinitesimal Rigidity Matroids on general embeddings is the same as the class of IRMs on generic embeddings 6. Every Infinitesimal Rigidity Matroid and Generic Rigidity Matroid is an Abstract Rigidity Matroid. In fact the relationship looks like Fig 1 1 Figure 1:...
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This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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lec11 - Geometric Constraints April 4, 6 & 11...

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