Extractors are strong expanders and have been proven extremely useful in derandomization tasks.
However, it is not known how to explicitly construct optimal extractors. We significantly improve previous results and achieve almost optimal extractors that work for sources with small entropy and extract all of the randomness from the given source. We are also able to improve previous applications by plugging in our new extractors to previous constructions. LogSpace reducible to the undirected s,t connectivity problem, is closed under complement. Table of Contents 1.