Splitters and near-optimal derandomization

  • Authors:
  • M. Naor;L. J. Schulman;A. Srinivasan

  • Affiliations:
  • -;-;-

  • Venue:
  • FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1995

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Abstract

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 2/sup k/ 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 /spl Sigma/II/spl Sigma/ 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.