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arXiv · 2301.13832

Bounds for c-Ideal Hashing

Fabian Frei·David Wehner
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Abstract

In this paper, we analyze hashing from a worst-case perspective. To this end, we study a new property of hash families that is strongly related to d-perfect hashing, namely c-ideality. On the one hand, this notion generalizes the definition of perfect hashing, which has been studied extensively; on the other hand, it provides a direct link to the notion of c-approximativity. We focus on the usually neglected case where the average load \alpha is at least 1 and prove upper and lower parametrized bounds on the minimal size of c-ideal hash families. As an aside, we show how c-ideality helps to analyze the advice complexity of hashing. The concept of advice, introduced a decade ago, lets us measure the information content of an online problem. We prove hashing's advice complexity to be linear in the hash table size.

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Fabian Frei, David Wehner. 2023-01-31. Bounds for c-Ideal Hashing. https://arxiv.org/abs/2301.13832

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