Friday, December 9, 2022 — 12:00 PM EST

Title: Approximation algorithm for stochastic k-TSP

Speaker: David Aleman
Affiliation: University of Waterloo
Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract: The input of the deterministic k-TSP problem consists of a metric complete graph with root p in which the nodes are assigned a fixed non-negative reward. The objective is to construct a p-rooted path of minimum length that collects total reward at least k. In this talk we will explore a stochastic variant of this problem in which the rewards assigned to the nodes are independent random variables, and the objective is to derive a policy that minimizes the expected length of a p-rooted path that collects total reward at least k. We will discuss approximation algorithms for this problem proposed in a paper by Ene, Nagarajan and Saket, and a paper by Jiang, Li, Liu and Singla.

Friday, December 9, 2022 — 3:30 PM EST

Titile: Global geometric reductions for some bottleneck questions in hardness of approximation

Speaker: Vijay Bhattiprolu
Affiliation: University of Waterloo
Location: MC 5501 or contact Eva Lee for Zoom link

Abstract: I will describe the classical "local gadget reduction" paradigm for proving hardness of approximation results and then list some important optimization problems that resist all such attacks. With a focus on problems that can be cast as quadratic maximization over convex sets, I will describe some successes in bypassing the aforementioned bottleneck using ideas from geometry. Time permitting I will also describe some compelling new frontiers where answering some questions in convex geometry could be the path forward.

Friday, December 16, 2022 — 3:30 PM EST

Title: Probabilistic root finding in code-based cryptography

Speaker: Daniel Panario
Affiliation: School of Mathematics and Statistics, Carleton University
Location: MC 5501 or contact Eva Lee for Zoom link

Abstract: Factorization of polynomials over finite fields, and the particular subproblem of finding roots of polynomials, have many applications in diverse areas such as computer algebra, cryptography and coding theory, among many others. In practice, fast factorization algorithms are probabilistic.

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