Perfect Hash Families: Probabilistic Methods and Explicit Constructions
نویسندگان
چکیده
منابع مشابه
Explicit constructions for perfect hash families
Let k, v, t be integers such that k ≥ v ≥ t ≥ 2. A perfect hash family PHF(N ; k, v, t) can be defined as an N × k array with entries from a set of v symbols such that every N× t subarray contains at least one row having distinct symbols. Perfect hash families have been studied by over 20 years and they find a wide range of applications in computer sciences and in cryptography. In this paper we...
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An (n; m; w)-perfect hash family is a set of functions F such that there exists at least one f 2 F such that fj X is one-to-one. Perfect hash families have been extensively studied by computer scientists for over 15 years, mainly from the point of view of constructing eecient algorithms. In this paper, we study perfect hash families from a com-binatorial viewpoint, and describe some new recursi...
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Let S be a set of functions with common domain D. We say X, a subset of D, an interpolation set for S if the values on X uniquely determine a function f in S. Recently, Piotr Indyk gave an explicit construction of interpolation sets of size O(k log n) for the family of boolean functions on n variables which depend symmetrically on at most k variables. Using perfect hash families, we have a vari...
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An (s; n; q; t)-perfect hash family is a set of functions 1 ; 2 ; : : :; s from a set V of cardinality n to a set F of cardinality q with the property that every t-subset of V is injectively mapped into F by at least one of the functions i. The paper shows that the maximum value n s;t (q) that n can take for xed s and t has a leading term that is linear in q if and only if t > s. Moreover, for ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3050