Efficient algorithms for discrepancy minimization in convex sets
نویسندگان
چکیده
منابع مشابه
Efficient Algorithms for Discrepancy Minimization in Convex Sets
A result of Spencer [16] states that every collection of n sets over a universe of size n has a coloring of the ground set with {−1,+1} of discrepancyO(√n). A geometric generalization of this result was given by Gluskin [10] (see also Giannopoulos [9]) who showed that every symmetric convex body K ⊆ R with Gaussian measure at least e−ǫn, for a small ǫ > 0, contains a point y ∈ K where a constan...
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A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O( √ n). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In fact, the LovettMeka algorithm finds a half integral point in any “large enough” polytope. However, their algorithm crucially relies on the facet structure and d...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832
DOI: 10.1002/rsa.20763