Title: Greedy algorithm for stochastic matching is a 2-approximatioSpeaker: Ian DeHaan Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link
Abstract: We will discuss the greedy algorithm for the stochastic matching problem. In this problem, we are given an undirected graph where each edge is assigned a probability p_e in [0, 1] and each vertex is assigned a patience t_v in Z+. We begin each step by probing an edge e which is not adjacent to any edges in our matching. The probe will succeed with probability p_e, and if it does, we add e to our matching. Otherwise, we may not probe e again. We also may not probe edges adjacent to a vertex v more than t_v times. The goal is to maximize the number of edges we add to our matching.
Title: Integer programs with bounded subdeterminants and two nonzeros per rowSpeaker: Stefan Weltge Affiliation: Technical University of Munich Location: MC 5501 or contact Eva Lee for Zoom link
Abstract: Determining the complexity of integer linear programs with integer coefficient matrices whose subdeterminants are bounded by a constant is currently a very actively discussed question in the field. In this talk, I will present a strongly polynomial-time algorithm for such integer programs with the further requirement that every constraint contains at most two variables. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles, where k is any constant. Previously, polynomial-time algorithms were only known for k = 0 (bipartite graphs) and for k = 1.
This is joint work with Samuel Fiorini, Gwenaël Joret, and Yelena Yuditsky, which recently appeared at FOCS this year.