Com S 633: Randomness in Computation Lecture 14 Scribe: Ankit Agrawal Summary: Com S 633: Randomness in Computation Lecture 14 Scribe: Ankit Agrawal 1 Derandomization We have seen various applications of randomization, wherein we were able to design simple and efficient algorithms for some (supposedly) deterministically hard problems. Now, we shall see whether randomness can be eliminated or at least reduced from these algorithms; and if so, how? Broadly, there are two ways of achieving derandomization: i) Algorithmic derandomization ii) Complexity theoretic derandomization Algorithmic derandomization techniques look at a particular randomized algorithm, and us- ing the inherent properties of the problem, analyze the randomized algorithm better to come up with ways to remove randomness from that algorithm. Here, we start with the original randomized algorithm for a particular problem, and improve it to derandomize it. Complexity theoretic derandomization techniques refer to a general strategy that can be used to remove randomness from a broad class of algorithms. Typically, this is done by pseudo-random generators, which produce random-looking bits. 1.1 Derandomizing Maxcut Max-Cut problem Given a graph G = (V, E),|V | = n, |E| = m, output two sets A and B s.t. AB = V, AB = Collections: Computer Technologies and Information Sciences