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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.” FordFulkerson’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 HarrisRoss rep
relatively largescale 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 MaxFlow MinCut 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.
 Spring '10
 HORTON
 Algorithms

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