lec7 - Geometric Constraint Lecture(Mar 6-8 Instructor...

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Unformatted text preview: Geometric Constraint Lecture(Mar 6-8) Instructor: Meera Sitharam, Recorded by Jianhua Fan Mar 11, 2006 1 Problem Categories Type One • Fixed Dimension • Partially Metric Space • Exact Realization (usually no distortion) • Generic or Nongeneric • Embedding in Euclidian/Projective/Informal Hyperbolic Space • General or Specail (especially for nongeneric) • Special Regular Input or General Input • Combinatorial or Algebraic Type Two • Min Dimension • Complete Metric Space • Distortion Allowed • Embedding in LP Space or other Metric Space • Symmetric Input or General Input • Combinatorial or Analytic 2 Five Questions 1. Given graph G , characterize d for which ( G, d ) has a realization. Here d are constraints, for example distance constraints. 1 2. Given graph G and constraints d , provide a realization. 3. Given grpah G , generically classify it into two categories: • It has nite number of realizations. One realization Many realizations • It has in nite number of realizations. 4. Given G , generically characterize the realization space. 5. Given nongeneric G , with xed or restricted d , answer question 3 and 4. Give the classi cation and description of its realization space. 3 Working on these Five Questions 3.1 Question 1 Problem: G is a complete distance graph, nd { d : ( G, d ) has a realization in R k space } . Theorem: Cayley-Menger conditions are the necessary and su cient conditions that ( G, d ) has a realization in R k space....
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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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lec7 - Geometric Constraint Lecture(Mar 6-8 Instructor...

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