Planar Partition Oracles for Bounded Degree Graphs in Polynomial Time

Explore a 34-minute lecture on planar partition oracles for bounded degree graphs, presented by Akash Kumar from IIT Bombay at the Simons Institute. Delve into the concept of hyperfinite decompositions for planar graphs with maximum degree d, where removing εdn edges results in connected components of size independent of n. Learn about partition oracles as crucial tools for sublinear algorithms and property testing, providing consistent access to hyperfinite decompositions without preprocessing. Discover a new partition oracle that runs in poly(d/ε) time and its application in developing a tester for all planar properties with a runtime of exp(d/ε^2). Gain insights into how this machinery builds upon the seminal work of Newman and Sohler, offering improved error analysis for sublinear graph simplification.