lecture15 - CS 473 Algorithms Chandra Chekuri...

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CS 473: Algorithms Chandra Chekuri [email protected] 3228 Siebel Center University of Illinois, Urbana-Champaign Fall 2009 Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow using capacity scaling algorithm in O ( m 2 log C ) time when capacities are integral Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow using capacity scaling algorithm in O ( m 2 log C ) time when capacities are integral using Edmonds-Karp algorithm in O ( m 2 n ) time when capacities are rational (strongly polynomial time algorithm) Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow using capacity scaling algorithm in O ( m 2 log C ) time when capacities are integral using Edmonds-Karp algorithm in O ( m 2 n ) time when capacities are rational (strongly polynomial time algorithm) if capacities are integral then there is a maximum flow that is integral and above algorithms give an integral max flow Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow using capacity scaling algorithm in O ( m 2 log C ) time when capacities are integral using Edmonds-Karp algorithm in O ( m 2 n ) time when capacities are rational (strongly polynomial time algorithm) if capacities are integral then there is a maximum flow that is integral and above algorithms give an integral max flow given a flow of value v , can decompose into O ( m + n ) flow paths of same total value v . integral flow implies integral flow on paths Chekuri CS473ug
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Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s - t flow can be computed using Ford-Fulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow using capacity scaling algorithm in O ( m 2 log C ) time when capacities are integral using Edmonds-Karp algorithm in O ( m 2 n ) time when capacities are rational (strongly polynomial time algorithm)
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