Dynamic Matching and Ordered Ruzsa-Szemerédi Graphs - Towards Constructive Matching Sparsifiers

Explore dynamic matching algorithms and Ruzsa-Szemerédi graphs in this lecture from the Simons Institute. Delve into the concept of matching sparsifiers and their importance in preserving large matchings in induced subgraphs. Learn about the non-constructive proof by Goel, Kapralov, and Khanna for sparse matching sparsifiers in bipartite graphs, and discover approaches to overcome its limitations. Examine conditionally fast dynamic algorithms for approximate matchings, with a focus on the fully dynamic setting where graphs undergo edge insertions and deletions. Gain insights into maintaining approximate maximum matchings efficiently in dynamic graphs. The lecture draws from recent research on fully dynamic matching, ordered Ruzsa-Szemerédi graphs, and the application of regularity lemma in streaming and dynamic matching problems.