NDLI: Tabulation-Based 5-Independent Hashing with Applications to Linear Probing and Second Moment Estimation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Thorup, Mikkel Zhang, Yin
Copyright Year	2012
Abstract	In the framework of Wegman and Carter, a k-independent hash function maps any k keys independently. It is known that 5-independent hashing provides good expected performance in applications such as linear probing and second moment estimation for data streams. The classic 5-independent hash function evaluates a degree 4 polynomial over a prime field containing the key domain $[n]=\{0,\ldots,n-1\}$. Here we present an efficient 5-independent hash function that uses no multiplications. Instead, for any parameter c, we make $2c-1$ lookups in tables of size $O(n^{1/c})$. In experiments on different computers, our scheme gained factors of 1.8 to 10 in speed over the polynomial method. We also conducted experiments on the performance of hash functions inside the above applications. In particular, we give realistic examples of inputs that make the most popular 2-independent hash function perform quite poorly. This illustrates the advantage of using schemes with provably good expected performance for all inputs.
Starting Page	293
Ending Page	331
Page Count	39
File Format	PDF
ISSN	00975397
DOI	10.1137/100800774
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	41
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-04-17
Access Restriction	Subscribed
Subject Keyword	Information storage and retrieval Analysis of algorithms and problem complexity tabulation Probability in computer science k-independence hashing Data structures Randomized algorithms Searching and sorting Analysis of algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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