A construction method for optimally universal hash families and its consequences for the existence of RBIBDs (extended abstract)

Abstract

We introduce a method for constructing optimally universal hash families and equivalently RBIBDs. As a consequence of our construction we obtain minimal optimally universal hash families, if the cardinalities of the universe and the range are powers of the same prime. A corollary of this result is that the necessary condition for the existence of an RBIBD with parameters (ν, κ, λ), namely ν mod κ = λ(ν - 1) mod (κ - 1) = 0, is sufficient, if ν and κ are powers of the same prime. As an application of our construction, we show that the κ-MAXCUT algorithm of Hofmeister and Lefmann [9] can be implemented such that it has a polynomial running time, in the case that the number of vertices and κ are powers of the same prime. © Springer-Verlag Berlin Heidelberg 2004.