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Unformatted text preview: R d . 4. Fixed d,generically classify : no solution, unique solution or nitely many solution. Note, in 3d, the above question is still open. Particularly, for what special class of graphs in d Dimension, we can classify it? For question 1, a randomized algorithm with high probability (1 (  a  )), nds an appropriate P + realization in approximately (1+ ) d min dimension d by running time T (  a  , 1 /, 1 , 1 / ). 1 3 NonDistance Constraint Very specif graphs (regular graphs) 4 Questions and Discussion 1. How to generate a random subspace oF dimension d in R n ? or example, we can sample two angles For 3D. How to sample 2d in R 4 ? 2. In 2d, the lasgest m s.t. (1). m points and m lines s.t. every pair oF points is seperated by exactly m/2 lines; (2). or maximum m, fnd all such realization? Modulo what? 2...
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 Fall '08
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 Geometry, Topology, Manifold, Euclidean space, Meera Sitharam

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