On theL2-Discrepancy for Anchored Boxes
نویسندگان
چکیده
منابع مشابه
On the L2-Discrepancy for Anchored Boxes
The L 2-discrepancy for anchored axis-parallel boxes has been used in several recent computational studies, mostly related to numerical integration, as a measure of the quality of uniform distribution of a given point set. We point out that if the number of points is not large enough in terms of the dimension (e.g., fewer than 10 4 points in dimension 30) then nearly the lowest possible L 2-dis...
متن کاملMaximum Volume Subset Selection for Anchored Boxes
Let B be a set of n axis-parallel boxes in R such that each box has a corner at the origin and the other corner in the positive quadrant of R, and let k be a positive integer. We study the problem of selecting k boxes in B that maximize the volume of the union of the selected boxes. The research is motivated by applications in skyline queries for databases and in multicriteria optimization, whe...
متن کاملCombinatorial Discrepancy for Boxes via the γ2 Norm
The γ2 norm of a realm×n matrix A is the minimum number t such that the column vectors of A are contained in a 0-centered ellipsoid E ⊆ R that in turn is contained in the hypercube [−t, t]. This classical quantity is polynomial-time computable and was proved by the second author and Talwar to approximate the hereditary discrepancy herdiscA as follows: γ2(A)/O(logm) ≤ herdiscA ≤ γ2(A) · O( √ log...
متن کاملTighter Bounds for the Discrepancy of Boxes and Polytopes
Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set P , and a collection F = {F1, ..., Fm} of subsets of P , and our goal is color P with two colors, red and blue, so that the largest absolute difference between the number of red elements and the...
متن کاملBracketing numbers for axis-parallel boxes and applications to geometric discrepancy
In the first part of this paper we derive lower bounds and constructive upper bounds for the bracketing numbers of anchored and unanchored axis-parallel boxes in the d-dimensional unit cube. In the second part we apply these results to geometric discrepancy. We derive upper bounds for the inverse of the star and the extreme discrepancy with explicitly given small constants and an optimal depend...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 1998
ISSN: 0885-064X
DOI: 10.1006/jcom.1998.0489