 
Summary: Derandomization via small sample spaces
Noga Alon
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact
Sciences, Tel Aviv University, Tel Aviv 69978, Israel. Email: noga@math.tau.ac.il.
Abstract
Many randomized algorithms run successfully even when the random choices
they utilize are not fully independent. For the analysis some limited amount of
independence, like kwise independence for some fixed k, often suffices. In these
cases, it is possible to replace the appropriate exponentially large sample spaces
required to simulate all random choices of the algorithms by ones of polynomial
size. This enables one to derandomize the algorithms, that is, convert them into
deterministic ones, by searching the relatively small sample spaces deterministi
cally. If a random variable attains a certain value with positive probability, then
we can actually search and find a point in which it attains such a value.
The observation that n1 pairwise independent nontrivial random variables
can be defined over a sample space of size n has been mentioned already long ago,
see [11], [23]. The pairwise independent case has been a crucial ingredient in the
construction of efficient hashing schemes in [14], [17]. A more general construc
tion, of small sample spaces supporting kwise independent random variables,
appeared in [19]. For the case of binary, uniform random variables this is treated
