@inproceedings{4b783b02d84a4da989b694425ab1eb23,
title = "On the beck-fiala conjecture for random set systems",
abstract = "Motivated by the Beck-Fiala conjecture, we study discrepancy bounds for random sparse set systems. Concretely, these are set systems (X, Σ), where each element x € X lies in t randomly selected sets of Σ, where t is an integer parameter. We provide new bounds in two regimes of parameters. We show that when |Σ| ≥ |X| the hereditary discrepancy of (X, Σ) is with high probability O(p t log t); and when |X| > |Σ|t the hereditary discrepancy of (X, Σ) is with high probability O(1). The first bound combines the Lov{\'a}sz Local Lemma with a new argument based on partial matchings; the second follows from an analysis of the lattice spanned by sparse vectors.",
keywords = "Beck-Fiala conjecture, Discrepancy theory, Random set systems",
author = "Esther Ezra and Shachar Lovett",
note = "Funding Information: E.E is supported by an NSF CAREER award 1553354. S.L. is supported by an NSF CAREER award 1350481 and a Sloan fellowship.; 19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016 ; Conference date: 07-09-2016 Through 09-09-2016",
year = "2016",
month = sep,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.59",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Klaus Jansen and Claire Mathieu and Rolim, {Jose D. P.} and Chris Umans",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 19th International Workshop, APPROX 2016 and 20th International Workshop, RANDOM 2016",
address = "ألمانيا",
}