Derandomization via small sample spaces

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 k-wise 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 deterministically. 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.