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 (v,k,λ), namely v mod k = λ(v–1) mod (k–1) = 0, is sufficient, if v and k are powers of the same prime. As an application of our construction, we show that the k-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 k are powers of the same prime.
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Woelfel, P. (2004). A Construction Method for Optimally Universal Hash Families and Its Consequences for the Existence of RBIBDs. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_5
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