Topic: dynamic data structures

Monika Henzinger surveys algorithms that maintain graph information as vertices and edges change. The lecture explains major algorithmic techniques and open problems, and shows how dynamic data structures support applications such as clustering and recent breakthroughs in static maximum-flow and minimum-cost-flow algorithms.

Aaron Sidford introduces recent advances towards nearly linear-time algorithms for fundamental computational problems. Examples include matching, maximum flow, minimum cuts, linear systems and linear programming. The lecture explains how continuous optimisation, dynamic data structures and sketching interact, often transferring techniques between apparently different settings.