The All-Pairs Max-Flow problem has gained significant popularity in the last two decades, and many results are known regarding its fine-grained complexity. Despite this, wide gaps remain in our understanding of the time complexity for several basic variants of the problem, including for directed or undirected graphs, with unit or arbitrary capacities, on the edges or on the nodes.
In this talk, I will describe some recent progress aiming to bridge this gap by providing algorithms, conditional lower bounds, and non-reducibility results.
Based on several joint works with Abhranil Chatterjee, Prerona Chatterjee, Mrinal Kumar and Adrian She.