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Graphs and Physical Models
Definitions and Fundamental Principles
Maximum Flow in Deterministic Graphs
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arbitrary assume assumption augmentation path branch capacities branch flows branch ij branches of G columns commodity compute connected Consider the graph constraints contains defined denote directed branches directed graph directed s-t distance matrix elements entries equation exists finite flow pattern flow problem function graph G graph in Fig graph shown Hamilton circuit Hence incidence matrix integer Labeling Algorithm least Lemma Let G linear program Max-Flow Min-Cut Theorem maximize maximum flow maximum flow problem min-cut matrix minimal minimum cost n-vertex nonnegative normal distribution number of branches number of vertices obtained optimum partitioned Prob probability distribution procedure proved random graph random variable realization s-t cut s-t flow s-t path satisfied Section semigraph Shortest Path shortest tree shown in Fig solution Step subgraph Suppose synthesis terminal capacity matrix Theorem triangle inequality Type I error undirected vector vertex cut-set weight zero