lecture_14

# lecture_14 - Faster maximum flow algorithms Notations n =...

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Faster maximum flow algorithms Notations. n = number of vertices; m = number of edges; integer C = max capacity. caling FF O(m 2 g C) time. Scaling FF : O(m log C) time. : O(m 2 n) time; edge capacity can be arbitrarily large real number. 2 m) or O(n 3 ) time. King, Rao & Tarjan: O(n m log n) time.

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Inefficiency of Ford and Fulkerson algorithm max flow = 2,000,000 s t v 1,000,000 1 1,000,000 u 1,000,000 1,000,000 s u t v 1 /1,000,000 1 1 /1,000,000 1,000,000 1,000,000 Flow value = 1
Inefficiency of Ford and Fulkerson algorithm residual network s t v 999,999 1 1,000,000 1 1 u 999,999 1,000,000 s u t v 999,999 1 999,999 1,000,000 1,000,000 1 1

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Inefficiency of Ford and Fulkerson algorithm augmenting path s t v 999,999 1 1,000,000 1 1 lue = 2 s u t v 1 /1,000,000 0 1 /1,000,000 1 /1,000,000 1 /1,000,000 u 999,999 1,000,000 value = 2
Inefficiency of Ford and Fulkerson algorithm residual network s t v 999,999 1 999,999 1 1 1 1 u 999,999 999,999 s u t v 999,999 1 999,999 999,999 999,999 1 1 1 1

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Inefficiency of Ford and Fulkerson algorithm lue = s t v 999,999 1 99,999 999,999 1 1 1 1 s u t v 2 /1,000,000 1 2 /1,000,000 1 /1,000,000 1 /1,000,000 value = 3 u 999,999 999,999
Scaling algorithm: find an augmenting path with large capacity. 2m log C augmentations and O(m 2 log C) time. Edmond & Karp: find the shortest path in terms of number of edges (breadth first search). mn augmentaions; O(m

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lecture_14 - Faster maximum flow algorithms Notations n =...

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