 
Summary: Balanced Families of Perfect Hash Functions
and Their Applications
Noga Alon1,
and Shai Gutner2,
1
Schools of Mathematics and Computer Science, TelAviv University, TelAviv,
69978, Israel
noga@math.tau.ac.il
2
School of Computer Science, TelAviv University, TelAviv, 69978, Israel
gutner@tau.ac.il
Abstract. The construction of perfect hash functions is a wellstudied
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 11 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 11 on S, for
each S of size k. In the new notion of balanced families, we require the
number of 11 functions to be almost the same (taking to be close to
