We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m^{1+o(1)} time. Our algorithm builds the flow through a sequence of m^{1+o(1)} approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m^{o(1)} time using a new dynamic graph data structure. Our framework extends to algorithms running in m^{1+o(1)} time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives almost-linear time algorithms for several problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and p-norm isotonic regression on arbitrary directed acyclic graphs.
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Concurrent-Flow Flame Spread in a Narrow Flow Duct in Microgravity – Effects of Flow Confinement and Radiation Reflection
- Award ID(s):
- 1740478
- PAR ID:
- 10313747
- Date Published:
- Journal Name:
- 12th U.S. National Combustion Meeting
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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