Title: Stochastic Load Balancing on Unrelated MachinesSpeaker: Rian Neogi Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link
Abstract: We will take a look at the stochastic load balancing problem. The goal is to assign tasks to machines, so that the maximum amount of time taken by any machine to complete all its assigned tasks is minimized. The stochastic twist to this problem is that now the time required to complete each task is a random variable sampled from some known distribution. For the stochastic version, we need to minimize the maximum time taken by any machine in expectation. We will look at a constant factor approximation algorithm for this problem that appeared in a recent paper by Gupta, Kumar, Nagarajan and Shen.
Title: Non-realizability of polytopes via linear programmingSpeaker: Amy Wiebe Affiliation: UBC Okanagan Location: MC 5501 or contact Melissa Cambridge for Zoom link
Abstract: A classical question in polytope theory is whether an abstract polytope can be realized as a concrete convex object. Beyond dimension 3, there seems to be no concise answer to this question in general. In specific instances, answering the question in the negative is often done via “final polynomials” introduced by Bokowski and Sturmfels. This method involves finding a polynomial which, based on the structure of a polytope if realizable, must be simultaneously zero and positive, a clear contradiction.