Bounds for c-Ideal Hashing

F. Frei, D. 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.
c-理想哈希的界
在本文中,我们从最坏情况的角度来分析哈希。为此,我们研究了哈希族的一个与d-完全哈希强相关的新性质,即c-理想性。一方面,这个概念推广了已经被广泛研究的完美哈希的定义;另一方面,它提供了与c近似概念的直接联系。我们将重点放在通常被忽略的情况下,即平均负载\ α至少为1,并证明c-理想哈希族最小大小的上下参数化界限。作为题外话,我们将展示c-ideal如何帮助分析哈希的通知复杂性。建议的概念是十年前提出的,它让我们能够衡量在线问题的信息内容。我们证明哈希的建议复杂度在哈希表的大小上是线性的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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