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arXiv · 1706.02783

Linear Hashing is Awesome

Mathias Bæk Tejs Knudsen
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Abstract

We consider the hash function $h(x) = ((ax+b) \bmod p) \bmod n$ where $a,b$ are chosen uniformly at random from $\{0,1,\ldots,p-1\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$ the expected length of the longest chain is $\tilde{O}\!\left(n^{1/3}\right)$. The proof also generalises to give the same bound when we use the multiply-shift hash function by Dietzfelbinger et al. [Journal of Algorithms 1997].

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Mathias Bæk Tejs Knudsen. 2017-06-08. Linear Hashing is Awesome. https://arxiv.org/abs/1706.02783

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