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Balanced Families of Perfect Hash Functions and Their Applications
 

Summary: Balanced Families of Perfect Hash Functions
and Their Applications
Noga Alon1,
and Shai Gutner2,
1
Schools of Mathematics and Computer Science, Tel-Aviv University, Tel-Aviv,
69978, Israel
noga@math.tau.ac.il
2
School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel
gutner@tau.ac.il
Abstract. The construction of perfect hash functions is a well-studied
topic. In this paper, this concept is generalized with the following defi-
nition. We say that a family of functions from [n] to [k] is a -balanced
(n, k)-family of perfect hash functions if for every S [n], |S| = k, the
number of functions that are 1-1 on S is between T/ and T for some
constant T > 0. The standard definition of a family of perfect hash func-
tions requires that there will be at least one function that is 1-1 on S, for
each S of size k. In the new notion of balanced families, we require the
number of 1-1 functions to be almost the same (taking to be close to

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics