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- W1529142014 abstract "Abstract 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 R n (the current best algorithm has complexity roughly n 4 , conjectured to be n 3 ). 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." @default.
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- W1529142014 date "2006-01-01" @default.
- W1529142014 modified "2023-09-27" @default.
- W1529142014 title "Dispersion of Mass and the Complexity of Randomized Geometric Algorithms." @default.
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