Online algorithms : the online job assignment problem and its variants

Abstract

Traditionally, algorithms try to find the optimal solution for a problem in a “three-phase” approach: fetch the input, run the algorithm, output the solution. But recently, there has been an interest in understanding algorithms “under uncertainty”: when you do not have all the input at once, or maybe you get an input with random noise, and so on. We will focus on the area of online algorithms, wherein the input to an algorithm arrives in a sequence (unknown to the algorithm), and at for each part of the input, the algorithm is forced to make irrevocable decisions. We first look at the Multiplicative Weights Update method, which is essentially an online algorithm. We understand how the abstraction of the multiplicative weights update method helps us solve constrained optimisation problems approximately but quickly. We then systematically study the Online Job Assignment or the Online Edge Orientation problem. We also look at some variants of the original problem. Finally, we look at the scope for future work in all these problems.