TY - JOUR

T1 - Is linear hashing good?

AU - Alon, Noga

AU - Dietzfelbinger, Martin

AU - Miltersen, Peter Bro

AU - Petrank, Erez

AU - Tardos, Gabor

PY - 1997

Y1 - 1997

N2 - Considering the set H of all linear (or affine) transformations between two vector spaces over a finite field F, the ability of H as a class of hash functions is studied. Hashing a set S of size n into a range, having the same cardinality n by a randomly chosen function from H and looking at the size of the largest hash bucket, is particularly evaluated. If the finite field F has n elements, then there is a bad set S⊂F2 of size n with expected minimal bucket size Ω(n1/3). If n is a perfect square there is a worse set with largest bucket size always at least √n. If however, the considered is the field of two elements then better bounds will be obtained. The best previously known upper bound was O(2√log n). This upper bound is reduced to θ(log n/log log n).

AB - Considering the set H of all linear (or affine) transformations between two vector spaces over a finite field F, the ability of H as a class of hash functions is studied. Hashing a set S of size n into a range, having the same cardinality n by a randomly chosen function from H and looking at the size of the largest hash bucket, is particularly evaluated. If the finite field F has n elements, then there is a bad set S⊂F2 of size n with expected minimal bucket size Ω(n1/3). If n is a perfect square there is a worse set with largest bucket size always at least √n. If however, the considered is the field of two elements then better bounds will be obtained. The best previously known upper bound was O(2√log n). This upper bound is reduced to θ(log n/log log n).

UR - http://www.scopus.com/inward/record.url?scp=0030645680&partnerID=8YFLogxK

U2 - 10.1145/258533.258639

DO - 10.1145/258533.258639

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AN - SCOPUS:0030645680

SN - 0734-9025

SP - 465

EP - 474

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing

Y2 - 4 May 1997 through 6 May 1997

ER -