Seminars & Colloquia Calendar

Abstract: Expanders enable us to make exciting progress in several areas of graph algorithms in the last few years. As examples, we show

(1) the first deterministic almost-linear time algorithms for solving Laplacian systems and computing approximate max flow (previous fast algorithms are randomized Monte Carlo),

(2) the first deterministic dynamic connectivity algorithm with subpolynomial worst-case update time (previous deterministic algorithms take \(\Omega(\sqrt{n})\) update time),

(3) the first near-linear time algorithm for computing an exact maximum bipartite matching in moderately dense graphs (previous algorithms take strictly superlinear time), and

(4) the first non-trivial example of distributed algorithms in the CONGEST model whose round-complexity matches the bound in the stronger CONGESTED CLIQUE model with no locality constraint. I will describe the key expander-related tools behind these applications and explain how to use them at a high-level. I will conclude with a list of open problems.

This survey talk is based on joint works with many people including Aaron Bernstein, Jan van den Brand, Yi-Jun Chang, Julia Chuzhoy, Yu Gao, Gramoz Goranci, Maximilian Probst Gutenberg, Yin Tat Lee, Jason Li, Danupon Nanongkai, Richard Peng, Harald Räcke, Aaron Sidford, Zhao Song, He Sun, Zihan Tan, Di Wang, and Christian Wulff-Nilsen.