Year: 2018
Type: preprint
Abstract: We study the placement of n balls into n bins where balls and bins are represented as two vector spaces over Z 2 . The placement is done according to a linear transformation between the two vector spaces. We analyze the expected size of a largest bin. The only currently known upper bound is O(log n log log n) by Alon et al. and holds for placing n log n balls into n bins. We show that this bound can be improved to O(log n) in the case when n balls are placed into n bins. We use the same basic technique as Alon et al. but give a tighter analysis for this case.
Source: arXiv (Cornell University)
Author: Babka, Martin
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2897426927