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Unformatted text preview: graph[i][i] should be zero for all i. // graph[i][j] should be "infinity" if edge (i, j) does not exist // otherwise, graph[i][j] is the weight of the edge (i, j) floydWarshall(); // now graph[i][j] is the length of the shortest path from i to j } Max flow Min Cut son [1] mention that the maximum flow problem was formulated to them by T.E. Harris as follows: simplified model of railway traf pinpointed this particular proble tral one suggested by the model “Consider a rail network connecting two cities by way of a number of intermediate cities, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given city to the other.” Ford-Fulkerson’s reference 11 port by Harris and Ross [3] en mentals of a Method for Evalua Capacities, dated 24 October 19 ten for the US Air Force. At our Pentagon downgraded it to ‘unc 21 May 1999. In fact, the Harris-Ross rep relatively large-scale maximum coming from the railway network ern Soviet Union and Eastern Eu lite countries’). And the interest Ross was not to find a maxim rather a minimum cut (‘interdic It inspired Ford and Fulkerson to their famous Max-Flow Min-Cut Theorem: The maximum amount of flow that can be sent along a network from a set of sources to a set of destinations, subject to a given capacity upper bound, is equal to the minimum capacity of the cuts of the network that separate all be solved is: imum amou...
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This note was uploaded on 02/25/2014 for the course CS 4102 taught by Professor Horton during the Spring '10 term at UVA.

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