On the dispersion of sparse grids

DOI10.1016/j.jco.2017.11.005zbMath1426.68275arXiv1709.02983OpenAlexW2962981545MaRDI QIDQ1704609

David Krieg

Publication date: 12 March 2018

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02983

zbMATH Keywords

dispersionsparse gridhigh-dimensional problemslargest empty box

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Combinatorial geometries and geometric closure systems (51D20)

Related Items (14)

Universal discretization ⋮ New bounds on the minimal dispersion ⋮ Minimal dispersion of large volume boxes in the cube ⋮ Deterministic constructions of high-dimensional sets with small dispersion ⋮ The area of empty axis-parallel boxes amidst 2-dimensional lattice points ⋮ An upper bound on the minimal dispersion ⋮ The minimal \(k\)-dispersion of point sets in high dimensions ⋮ On the fixed volume discrepancy of the Fibonacci sets in the integral norms ⋮ Expected dispersion of uniformly distributed points ⋮ Improved dispersion bounds for modified Fibonacci lattices ⋮ Piercing all translates of a set of axis-parallel rectangles ⋮ Recovery algorithms for high-dimensional rank one tensors ⋮ A remark on the minimal dispersion ⋮ Piercing all translates of a set of axis-parallel rectangles

Cites Work

• Tractability of multivariate problems. Volume II: Standard information for functionals.
• A note on minimal dispersion of point sets in the unit cube
• An upper bound on the minimal dispersion
• Quasi-Monte-Carlo methods and the dispersion of point sequences
• On the largest empty axis-parallel box amidst \(n\) points
• On the size of the largest empty box amidst a point set
• Learnability and the Vapnik-Chervonenkis dimension
• Tractability of the approximation of high-dimensional rank one tensors

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