Explore a 28-minute lecture on incorporating nested dissection-based data structures into the Interior Point Method (IPM) framework for efficient Linear Programming (LP) solvers. Delve into applications for planar min-cost flow, planar k-multicommodity flow, LPs with low treewidth, and general separable LPs. Learn how these techniques enhance optimization algorithms for various problem types. Gain insights from Sally Dong of the University of Washington as she presents this talk as part of the Optimization and Algorithm Design series at the Simons Institute.