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Unformatted text preview: CS 473: Algorithms Chandra Chekuri [email protected] 3228 Siebel Center University of Illinois, UrbanaChampaign Fall 2009 Chekuri CS473ug 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 Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson algorithm in O ( mC ) time when capacities are integral and C is an upper bound on the flow Chekuri CS473ug Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson 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 Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson 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 EdmondsKarp algorithm in O ( m 2 n ) time when capacities are rational (strongly polynomial time algorithm) Chekuri CS473ug Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson 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 EdmondsKarp 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 Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson 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 EdmondsKarp 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 Network Flow: Facts to Remember Flow network: directed graph G , capacities c , source s , sink t maximum s t flow can be computed using FordFulkerson 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 EdmondsKarp algorithm in...
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Chekuri,C
 Algorithms

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