We discuss two probabilistic tools that have been successfully applied
in the analysis of randomized sequential algorithms, namely, the
FKG inequality, and deterministic construction of (almost)
random permutations. We show how these tools can be applied to obtain
efficient parallel algorithms for fundamental problems on
Based on joint work with Aravind Srinivasan.
Noga Alon and Moni Naor.
Derandomization, witnesses for Boolean matrix multiplication and
construction of perfect hash functions.
Algorithmica, 16(4-5):434-449, 1996.
C. M. Fortuin, P. W. Kasteleyn, and Jean Ginibre.
Correlation inequalities on some partially ordered sets.
Comm. Math. Phys., 22:89-103, 1971.
The probabilistic lens: Sperner, Turán and Bregman revisited.
In A tribute to Paul Erdos, pages 391-396. Cambridge Univ.
Press, Cambridge, 1990.
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