Sparsification: Graphs, CSPs and Codes - Sublinear Graph Simplification

Explore the concept of sparsification in graphs, constraint satisfaction problems (CSPs), and codes in this 49-minute lecture by Madhu Sudan from Harvard University. Delve into the history of graph sparsification, starting with the seminal works of Karger and Benczur in the 1990s. Examine how graphs can be compressed to nearly linear size while preserving cut information. Investigate the broader notion of structure sparsification with respect to query classes. Learn about CSP sparsification as proposed by Kogan and Krauthgamer in 2015, which unifies various sparsification problems. Discover the introduction of code sparsification as a new class of problems, abstracting techniques from graph sparsification. Explore how this generalization resolves questions in CSP sparsification and leads to a complete classification of symmetric Boolean CSPs allowing nearly linear sized sparsification. Gain insights into the latest developments in this field, including joint work with Sanjeev Khanna and Aaron Putterman.