@article {17595,
	title = {Explicit OR-dispersers with polylogarithmic degree},
	journal = {Journal of the ACM (JACM)},
	volume = {45},
	year = {1998},
	month = {1998/01//},
	pages = {123 - 154},
	abstract = {An (N, M, T)-OR-disperser is a bipartite multigraph G=(V, W, E) with |V| = N, and |W| = M, having the following expansion property: any subset of V having at least T vertices has a neighbor set of size at least M/2. For any pair of constants \&xgr;, \&lgr;, 1 >= \&xgr; > \&lgr; >= 0, any sufficiently large N, and for any T >= 2(logN) M <= 2(log N)\&lgr;, we give an explicit elementary construction of an (N, M,    T)-OR-disperser such that the out-degree of any vertex in V is at most polylogarithmic in N. Using this with known applications of OR-dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for any fixed \&eegr; > 0, we give the first polynomial-time simulation of RP algorithms using the output of any {\textquotedblleft}\&eegr;-minimally random{\textquotedblright} source. For any integral R > 0, such a source accepts a single request for an R-bit string and generates the string according to a distribution that assigns probability at most 2-R\&eegr; to any string. It is minimally random in the sense that  any weaker source is insufficient to do a black-box polynomial-time simulation of RP algorithms.},
	keywords = {derandomization, expander graphs, explicit constructions, hardness of approximation, hashing lemmas, imperfect sources of randomness, measures of information, pseudo-random generators, randomized computation, time-space tradeoffs},
	isbn = {0004-5411},
	doi = {10.1145/273865.273915},
	url = {http://doi.acm.org/10.1145/273865.273915},
	author = {Saks,Michael and Srinivasan, Aravind and Zhou,Shiyu}
}
@conference {17660,
	title = {Splitters and near-optimal derandomization},
	booktitle = {, 36th Annual Symposium on Foundations of Computer Science, 1995. Proceedings},
	year = {1995},
	month = {1995/10/23/25},
	pages = {182 - 191},
	publisher = {IEEE},
	organization = {IEEE},
	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 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},
	keywords = {Boosting, 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},
	isbn = {0-8186-7183-1},
	doi = {10.1109/SFCS.1995.492475},
	author = {Naor,M. and Schulman,L. J and Srinivasan, Aravind}
}
