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).
|Number of pages
|Conference Proceedings of the Annual ACM Symposium on Theory of Computing
|Published - 1997
|Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA
Duration: 4 May 1997 → 6 May 1997