Proceedings of IEEE 36th Annual Foundations of Computer Science (1995)
Oct. 23, 1995 to Oct. 25, 1995
M. Naor , Dept. of Appl. Math. & Comput. Sci., Weizmann Inst. of Sci., Rehovot, Israel
L.J. Schulman , Dept. of Appl. Math. & Comput. Sci., Weizmann Inst. of Sci., Rehovot, Israel
A. Srinivasan , Dept. of Appl. Math. & Comput. Sci., Weizmann Inst. of Sci., Rehovot, Israel
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.
computational linguistics; randomised algorithms; probability; computational complexity; splitters; near-optimal derandomization; fairly general method; k-restrictions; probabilistic bound; near-optimal constructions; derandomization; learning; fixed-subgraph finding algorithms; hardness of approximation; set cover; deterministic constructions; local-coloring protocol; exhaustive testing
L. Schulman, M. Naor and A. Srinivasan, "Splitters and near-optimal derandomization," Proceedings of IEEE 36th Annual Foundations of Computer Science(FOCS), Milwaukee, Wisconsin, 1995, pp. 182.