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DIMACS Theory of Computing Seminar

Recent Applications of Expanders to Graph Algorithms

Thatchaphol Saranurak (TTIC/U Mich)

Date & time: Wednesday, 21 October 2020 at 11:00AM - 12:00PM

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 R├Ącke, Aaron Sidford, Zhao Song, He Sun, Zihan Tan, Di Wang, and Christian Wulff-Nilsen.

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