Splitters and near-optimal derandomization

TitleSplitters and near-optimal derandomization
Publication TypeConference Papers
Year of Publication1995
AuthorsNaor M, Schulman LJ, Srinivasan A
Conference Name, 36th Annual Symposium on Foundations of Computer Science, 1995. Proceedings
Date Published1995/10/23/25
ISBN Number0-8186-7183-1
KeywordsBoosting, Circuit testing, computational complexity, computational linguistics, Computer science, Contracts, derandomization, deterministic constructions, Educational institutions, Engineering profession, exhaustive testing, fairly general method, fixed-subgraph finding algorithms, hardness of approximation, Information systems, k-restrictions, learning, local-coloring protocol, MATHEMATICS, near-optimal constructions, near-optimal derandomization, Parallel algorithms, probabilistic bound, probability, Protocols, randomised algorithms, Set cover, splitters

We present a fairly general method for finding deterministic constructions obeying what we call k-restrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n,k)-universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2k configurations appear) and families of perfect hash functions. The near-optimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal ΣIIΣ threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a local-coloring protocol, and for exhaustive testing of circuits