Algos - 1 Chapter 26 Maximum Flow How do we transport the...

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Unformatted text preview: 1 Chapter 26 Maximum Flow How do we transport the maximum amount data from source to sink? Some of these slides are adapted from Lecture Notes of Kevin Wayne. Contents ¡ Contents. ¡ Maximum flow problem. ¡ Minimum cut problem. ¡ Max-flow min-cut theorem. ¡ Augmenting path algorithm. ¡ Capacity-scaling. ¡ Shortest augmenting path. Networks communication Network telephone exchanges, computers, satellites Nodes Arcs cables, fiber optics, microwave relays Flow voice, video, packets circuits gates, registers, processors wires current mechanical joints rods, beams, springs heat, energy hydraulic reservoirs, pumping stations, lakes pipelines fluid, oil financial stocks, currency transactions money transportation airports, rail yards, street intersections highways, railbeds, airway routes freight, vehicles, passengers chemical sites bonds energy biological genes pathways interactions ¡ Max flow and min cut. ¡ Two very rich algorithmic problems. ¡ Cornerstone problem in combinatorial optimization. ¡ Beautiful mathematical duality. ¡ Nontrivial applications / reductions. ¡ Network connectivity. ¡ Bipartite matching. ¡ Data mining. ¡ Image processing. ¡ Airline scheduling. ¡ Project selection. ¡ Network reliability. ¡ Security of statistical data. ¡ Distributed computing. ¡ Egalitarian stable matching. ¡ Distributed computing. ¡ Computational biology....
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Algos - 1 Chapter 26 Maximum Flow How do we transport the...

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