In this episode, Professor Pål Grønås Drange from the University of Bergen, introduces the field of Parameterized Complexity - a powerful framework for tackling hard computational problems by focusing on specific structural aspects of the input. This framework allows researchers to solve NP-complete problems more efficiently when certain parameters, like the structure of the graph, are "well-behaved".

At the center of the discussion is the network diversion problem, where the goal isn't to block all routes between two points in a network, but to force flow - such as traffic, electricity, or data - through a specific path. While this problem appears deceptively similar to the classic "Min.Cut/Max.Flow" algorithm, it turns out to be much harder and, in general, its complexity is still unknown. Parameterized complexity plays a key role here by offering ways to make the problem tractable under constraints like low treewidth or planarity, which often exist in real-world networks like road systems or utility grids.

Listeners will learn how vulnerability measures help identify weak points in networks, such as geopolitical infrastructure (e.g., gas pipelines like Nord Stream).

Follow out guest: Pål Grønås Drange