Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 30, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Saeed Ilchi

Derandomized balanced allocation

In this talk, we study the maximum loads of explicit hash families in the d-choice schemes when allocating sequentially n balls into n bins. We consider the Uniform-Greedy scheme which provides d independent bins for each ball and places the ball into the bin with the least load. We construct a hash family with O(log n log log n) random bits. The maximum loads of our hash family match the maximum loads of a perfectly random hash function in the Uniform-Greedy scheme, up to the low order term of constants. Previously, the best known hash families matching the same maximum loads of a perfectly random hash function in d-choice schemes were O(log n)-wise independent functions, which needs O(log² n) random bits. This talk is based on [1].

[1] Chen, Xue. "Derandomized balanced allocation." Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2019.

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