Lecture IX RANDOMIZATION AND DERANDOMIZATION

Notes on Complexity Theory Last updated : November , 2011 Lecture 25

Randomization provides unconditional benefits in many settings; examples include cryptography (where random keys are used to provide protection against an adversary) and distributed computing (where randomness can be used as a means to break symmetry between parties). Randomness also appears to help in algorithm design. But is it possible that, from a complexity-theoretic perspective, randomnes...

Derandomization and Circuit Lower Bounds

1 Introduction Primality testing is the following problem: Given a number n in binary, decide whether n is prime. In 1977, Solovay and Strassen [SS77] proposed a new type of algorithm for testing whether a given number is a prime, the celebrated randomized Solovay-Strassen primality test. This test and similar ones proved to be very useful. This fact changed the common notion of " feasible comp...

Randomization and derandomization

Randomization, Derandomization and Antirandomization: Three Games

Spencer, J., Randomization, derandomization and antirandomization: three games. Theoretical Computer Science 131 (1994) 415-429. Three games are given between two players, Paul and Carole, with a common theme. In each round Paul does a split and Carole chooses. Random play by Carole allows a bound for the game value. Through derandomization this becomes a deterministic strategy for Carole minim...

Deterministic Algorithms for Submodular Maximization Problems

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algor...