Factorization Norms and Hereditary Discrepancy
نویسندگان
چکیده
منابع مشابه
Factorization Norms and Hereditary Discrepancy
The ellipsoid-infinity norm of a real m × n matrix A, denoted by ‖A‖E∞, is the minimum `∞ norm of an 0-centered ellipsoid E ⊆ R that contains all column vectors of A. This quantity, introduced by the second author and Talwar in 2013, is polynomial-time computable and approximates the hereditary discrepancy herdiscA as follows: ‖A‖E∞/O(logm) ≤ herdiscA ≤ ‖A‖E∞ ·O( √ logm). Here we show that both...
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Let A be a m n{matrix. Linear and hereditary discrepancy are deened as lindisc(A) := maxfminfkA(p ")k 1 j " 2 ff1; 1g n g jp 2 1; 1] n g herdisc(A) := maxfminfk(a ij) i2m];j2J "k 1 j " 2 ff1; 1g n g jJ n]g: We're investigating connections between the two concepts. Best results known are lindisc(A) 2(1 2 2 n) herdisc(A) for any matrix A and an example of an A satisfying lindisc(A) = 2(1 1 n+1) h...
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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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The Discrepancy of a hypergraph is the minimum attainable value, over twocolorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a restriction of the hypergraph to a subset of its vertices, is a measure of its complexity. Lovász, Spencer and Vesztergombi (1986) related the natural extension ...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2018
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rny033