lecture14 - CS 473 Algorithms Chandra Chekuri...

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Unformatted text preview: CS 473: Algorithms Chandra Chekuri [email protected] 3228 Siebel Center University of Illinois, Urbana-Champaign Fall 2009 Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Part I Algorithm(s) for Maximum Flow Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach s v u t 10 20 20 10 30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach s v u t 10/10 20 10/20 10 30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach s v u t 10/10 10/20 10/20 10/10 30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach s v u t 10/10 20/20 20/20 10/10 10/30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach: Issues s v u t 10 20 20 10 30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach: Issues s v u t 10 20/20 20/20 10 20/30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach: Issues s v u t 10 20/20 20/20 10 20/30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible. Greedy can get stuck in sub-optimal flow! Chekuri CS473ug Ford-Fulkerson Algorithm Correctness and Analysis Polynomial Time Algorithms Greedy Approach: Issues s v u t 10 20/20 20/20 10 20/30 1 Begin with f ( e ) = 0 for each edge 2 Find a s- t path P with f ( e ) < c ( e ) for every edge e ∈ P 3 Augment flow along this path 4 Repeat augmentation for as long as possible....
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lecture14 - CS 473 Algorithms Chandra Chekuri...

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