On the discrepancy of random low degree set systems

SODA '19: Symposium on Discrete Algorithms San Diego California January, 2019, pp. 2557-2564, 2019.

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Abstract:

Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are n elements and m sets and each element lies in t randomly chosen sets. In this setting, Ezra and Lovett showed an O((t log t)1/2) discrepancy bound in the regime when n ≤ m and an O(1) bound when n 3 » mt. In this paper, we give a tight [MATH...More

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