Almost-optimal parallel algorithms for exact maximum flow on directed graphs

Develop an almost-optimal parallel algorithm for exact maximum flow on general directed graphs that achieves m^{1+o(1)} work and m^{o(1)} depth in the parallel setting.

Background

The authors construct congestion-preserving DAG projections and show an efficient parallel reduction from exact maximum flow on directed graphs to n^{o(1)}-approximate maximum flow on DAGs with near-optimal overhead. This positions the open problem within a simpler setting whose resolution would yield the desired almost-optimal parallel exact algorithm.

While near-optimal parallel bounds exist for approximate flow in special cases, achieving almost-optimal parallel work and depth for exact max flow on general directed graphs remains a central open challenge; the paper explicitly presents it as a major open problem and reduces it to approximation on DAGs.