Randomized Algorithms

Abstract

We look into randomized approaches for dealing with computational problems. A randomized algorithm uses random decisions to guide its computation. Its quality is measured in a worst-case manner over all instances by a probability distribution over the taken random decisions. We analyze different design methods and error models.

Objective

To systematically acquire an overview of the methods for designing randomized algorithms. To get deeper knowledge of the classification of randomized algorithms according to error models. To learn how to analyze the error probability of randomized algorithms.To learn about typical applications for randomized computations.

Content

In this seminar, we discuss how randomization can help to speed up algorithms for various computational problems. In the kick-off meeting, we will give a brief overview of modeling and classifying randomized algorithms. Then, each participant will study one aspect of this topic, following a specific scientific publication, and will give a presentation about this topic. The topics will include design methods for randomized algorithms like fingerprinting, foiling an adversary, random sampling, randomized rounding as well as the classification of randomized algorithms according to their error (e.g., Las Vegas vs. Monte Carlo algorithms). The considered problems will include, among others, hashing, primality testing, communication protocols, maximum satisfiability.

Resources