Derandomization

Abstract

Probabilistic thinking turns out to be uncannily effective for proving the existence of combinatorial objects. Such proofs can often be converted into randomized algorithms. There exist efficient randomized algorithms for prob- lems that are not known to have efficient deterministic solutions. Even when both deterministic as well as randomized algorithms are available for a prob- lem, the randomized algorithm is usually simpler. This fact may be enough to favor the randomized algorithm in practice. Sometimes, the route to deter- ministic solution is via a randomized one: after a randomized algorithm has been discovered, we may be able to remove the use of randomness. We will illustrate such “derandomization” techniques.