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2006
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Dispersion of Mass and the Complexity of Randomized Geometric Algorithms

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Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex geometry. We obtain a nearly quadratic lower bound on the complexity of randomized volume algorithms for convex bodies in Rn (the current best algorithm has complexity roughly n4 , conjectured to be n3 ). Our main tools, dispersion of random determinants and dispersion of the length of a random point from a convex body, are of independent interest and applicable more generally; in particular, the latter is closely related to the variance hypothesis from convex geometry. This geometric dispersion also leads to lower bounds for matrix problems and property testing. ∗ Supported by NSF ITR-0312354. † Supported in part by a Guggenheim fellowship.
Luis Rademacher, Santosh Vempala
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors Luis Rademacher, Santosh Vempala
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