Derandomization of dimensionality reduction and SDP based algorithms

We present two results on derandomization of randomized algorithms. The first result is a derandomization of the Johnson-Lindenstrauss (JL) lemma based randomized dimensionality reduction algorithm. Our algorithm is simpler and faster than known algorithms. It is based on deriving a pessimistic estimator of the probability of failure. The second result is a general technique for derandomizing semidefinite programming (SDP) based approximation algorithms. We apply this technique to the randomized algorithm for Max Cut. Once again the algorithm is faster than known deterministic algorithms for the same approximation ratio. For this problem we present a technique to approximate probabilities with bounded error.