Approximations and randomization

Abstract

In response to the apparent intractability of NP-hard problems, approximation algorithms were introduced as a way to provide strong guarantees about the quality of solutions, without requiring exponential time to obtain them. The study of randomized algorithms, procedures that “flip coins” and are allowed to err with some probability, arose alongside approximation algorithms as a possible resource for circumventing intractability. We outline some of the various types of approximation algorithms that have been proposed, with a special focus on ones using randomization, and suggest further research directions in this area.