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New bounds for perfect hashing via information theory. (English) Zbl 0676.68007
Körner and Marton consider the problem of finding bounds for the largest size of a k-separated subset for a family of perfect hash- functions. By extending an information theoretic bounding technique based on graph entropy to more general structures they are able to improve the Fredman-Komlòs [M. Fredman and J. Komlòs, On the size of separating systems and perfect hash functions, SIAM J. Algebraic Discrete Methods 5, 61-68 (1984; Zbl 0525.68037) bounds in several cases: They give a new lower bound for the size of a 3-separated subset on a 3- element alphabet, namely \[ 1/t\quad \log N(t,3,3)\gtrsim 1/4 \log 9/5 \] and they present better bounds for a subclass of problems which includes a 3-separated subset on a 3-element alphabet as a special case. For all k-separated subsets on k-element alphabets with \(k>3\) they could not improve the Fredman-Komlòs bounds.
Reviewer: W.Janko

MSC:
68P05 Data structures
68Q25 Analysis of algorithms and problem complexity
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[1] Fredman, M.; Komlos, J., On the size of separating systems and perfect hash functions, SIAM J. algebraic discr. meth, 5, 61-68, (1984) · Zbl 0525.68037
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