Constructive Discrepancy Minimization for Convex Sets
نویسندگان
چکیده
منابع مشابه
Constructive discrepancy minimization for convex sets
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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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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In terms of applications, the min discrepancy problem appears in many varied areas of both Computer Science (Computational Geometry, Comb. Optimization, Monte-Carlo simulation, Machine learning, Complexity, Pseudo-Randomness) and Mathematics (Dynamical Systems, Combinatorics, Mathematical Finance, Number Theory, Ramsey Theory, Algebra, Measure Theory,...). One may consult any of the following b...
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In discrepancy minimization problems, we are given a family of sets S = {S1, . . . , Sm}, with each Si ∈ S a subset of some universe U = {u1, . . . , un} of n elements. The goal is to find a coloring χ : U → {−1,+1} of the elements of U such that each set S ∈ S is colored as evenly as possible. Two classic measures of discrepancy are l∞-discrepancy defined as disc∞(S , χ) := maxS∈S | ∑ ui∈S χ(u...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2017
ISSN: 0097-5397,1095-7111
DOI: 10.1137/141000282