COMP 6651 Fall 2013 B Jaumard 45 Dynamic Prog Assembly Line Scheduling Knapsack

Comp 6651 fall 2013 b jaumard 45 dynamic prog

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COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 1 First selected node: u 0 source node S = { u 0 } Q = { u 1 , u 2 , u 3 , u 4 , u 5 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 2 Perform relaxation on outgoing edges of u 0 . COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 3 Node u 5 = arg min { Q } = 8 is selected. Note that all predecessors of u 5 are in S . Q = { u 1 , u 2 , u 3 , u 4 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 4 Perform relaxation on outgoing edges of the selected node: u 5 COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 5 Node u 2 = arg min { Q } = 13 is selected Note that all predecessors of u 2 belong to S S = { u 0 , u 2 , u 5 } Q = { u 1 , u 3 , u 4 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 6 No further edge relaxation Node u 4 = arg min { Q } = 15 is selected Q = { u 1 , u 3 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 7 Perform relaxation on outgoing edges of the last selected node: u 4 COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 8 Node u 1 = arg min { Q } = 18 is selected Q = { u 3 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 9 No possible further edge relaxation. COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 10 Q = { u 3 } COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 11 Node u 3 = arg min { Q } = 20 is selected Q = {} COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . . Longest Common Subseq. . . . Conclusions Dijkstra’Algorithm: An example Iteration 12 No possible relaxation COMP 6651 / Fall 2013 - B. Jaumard 45
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. . . . . . . . . . Dynamic Prog. . . . . . . . . . . . . . . . . Assembly-Line Scheduling . . . . . . . . . . . . . . Knapsack Pb . . . . . . . . . Shortest Path . . . . . . . . . . . . . . . . . .
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