Breadth first search animation

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Presentation transcript:

Breadth first search animation Network Optimization Breadth First Search Get ahold of a network, and use the same network to illustrate the shortest path problem for communication newtorks, the max flow problem, the minimum cost flow problem, and the multicommodity flow problem. This will be a very efficient way of introducing the four problems. (Perhaps under 10 minutes of class time.) Breadth first search animation

Breadth first search animation Initialize 1 2 4 5 3 6 9 7 8 1 2 4 5 3 6 9 7 8 1 1 Unmark all nodes in N; Mark node 1 and add it to LIST. LIST 1 Breadth first search animation

Breadth first search animation Select node 1 1 2 4 5 3 6 9 7 8 1 2 1 1 1 3 Select the first node in LIST. Arc numbers for arcs in A(i) refer to the order in which arcs of A(i) are scanned. LIST 1 Breadth first search animation

Breadth first search animation Scan arcs (1,2) 2 4 2 2 8 1 2 1 1 1 1 5 7 Find an admissible arc 3 9 3 6 LIST 1 2 Breadth first search animation

Breadth first search animation Scan arc (1,5) 2 4 2 2 8 1 2 1 1 1 1 5 5 7 3 Select node 1 and find an admissible arc. 3 9 3 6 LIST 1 2 5 Breadth first search animation

Breadth first search animation Scan arc (1,3) 2 4 2 2 8 1 2 1 1 1 1 5 5 7 3 Select node 1 and find an admissible arc. 3 9 3 3 6 4 LIST 1 2 5 3 Breadth first search animation

Breadth first search animation Delete Node 1 from LIST 2 4 2 2 8 1 1 1 1 1 5 5 7 3 Delete node 1 from LIST 9 3 3 6 4 LIST 1 2 5 3 Breadth first search animation

Breadth first search animation Select Node 2 1 2 4 2 2 2 8 2 1 1 1 1 1 5 5 7 3 Select first node on LIST 9 3 3 6 4 LIST 1 2 5 3 Breadth first search animation

Breadth first search animation Scan arc (2, 4) 5 1 2 4 4 2 2 2 8 2 1 1 1 5 5 7 3 Select an admissible arc 9 3 3 6 4 LIST 1 2 5 3 4 Breadth first search animation

Breadth first search animation Scan arc (2, 5) 5 1 2 4 4 2 2 2 8 2 1 1 1 5 5 7 3 Ignore any scanned arcs out of node 2 that are not admissible. 9 3 3 6 4 LIST 1 2 5 3 4 Breadth first search animation

Breadth first search animation Delete node 2 5 2 4 4 2 2 2 2 8 1 1 1 5 5 7 3 Delete node 2 from LIST 1 9 3 3 6 4 LIST 2 5 3 4 Breadth first search animation

Breadth first search animation Select node 5 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3 1 Select the first node on LIST 9 3 3 6 4 LIST 5 3 4 Breadth first search animation

Breadth first search animation Scan arc (5,6) 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3 Find an admissible arc 1 9 3 3 6 6 4 6 LIST 5 3 4 6 Breadth first search animation

Breadth first search animation Delete node 5 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1 Delete node 5 from LIST 2 9 3 3 6 6 4 6 LIST 5 3 4 6 Breadth first search animation

Breadth first search animation Select node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1 Select first node on LIST 2 9 3 3 3 6 6 4 6 LIST 3 4 6 Breadth first search animation

Breadth first search animation Scan arcs out of node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1 Ignore any scanned arc that is not admissible. 2 9 3 3 3 6 6 4 6 LIST 3 4 6 Breadth first search animation

Breadth first search animation Delete node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 Delete node 3 from LIST 9 3 3 3 3 6 6 4 6 LIST 3 4 6 Breadth first search animation

Breadth first search animation Select node 4 5 1 2 4 4 4 2 2 8 2 1 1 1 5 5 7 3 Select the first node on LIST 9 3 3 6 6 4 6 LIST 4 6 Breadth first search animation

Breadth first search animation Scan arc (4, 8) 5 1 2 4 4 4 7 2 2 8 8 2 1 1 1 5 5 7 3 Look for an admissible arc. 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 8 Breadth first search animation

Breadth first search animation Scan arc (4, 5) 5 1 2 4 4 4 7 2 2 8 8 2 1 1 1 5 5 7 3 Look for an admissible arc 9 3 3 6 6 4 6 LIST 4 6 8 Breadth first search animation

Breadth first search animation Delete Node 4 5 2 4 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3 Delete node 4 from LIST 9 3 3 6 6 4 6 LIST 4 6 8 Breadth first search animation

Breadth first search animation Select node 6 5 2 4 4 7 2 2 8 8 1 1 1 5 5 7 3 1 Select the first node on LIST 2 9 3 3 6 6 6 4 6 LIST 6 8 Breadth first search animation

Breadth first search animation Scan arc (6,7) 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 1 Scan arcs out of node 6 one at a time. 2 9 3 3 6 6 6 4 6 LIST 1 2 5 3 4 6 8 7 Breadth first search animation

Breadth first search animation Scan arc (6,9) 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 1 Scan arcs out of node 6 one at a time. 2 9 9 3 3 6 6 6 4 9 6 LIST 6 8 7 9 Breadth first search animation

Breadth first search animation Delete node 6 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 Delete node 6 from LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 6 8 7 9 Breadth first search animation

Breadth first search animation Select node 8 5 2 4 4 7 2 2 8 8 8 1 8 1 1 5 5 7 7 3 Select first node on LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 8 7 9 Breadth first search animation

Breadth first search animation Delete node 8 5 2 4 4 7 2 2 8 8 8 8 1 8 1 1 5 5 7 7 3 Delete node 8 9 9 3 3 6 6 6 6 4 9 6 LIST 8 7 9 Breadth first search animation

Breadth first search animation Select node 7 5 2 4 4 7 2 2 8 8 2 3 1 1 8 1 1 5 5 7 7 7 3 Select first node on LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 7 9 Breadth first search animation

Breadth first search animation Scan arcs out of node 7 5 2 4 4 7 2 2 8 8 2 3 1 1 8 1 1 5 5 7 7 7 3 Scan arcs out of node 7 one at a time. 9 9 3 3 6 6 6 6 4 9 6 LIST 7 9 Breadth first search animation

Breadth first search animation Delete node 7 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 7 7 3 Delete node 7 from LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 7 9 Breadth first search animation

Breadth first search animation Select node 9 5 2 4 4 7 2 2 8 8 2 1 8 1 1 5 5 7 7 3 Select the first node on LIST 1 9 9 9 3 3 6 6 6 6 4 9 6 LIST 9 Breadth first search animation

Breadth first search animation Scan arcs out of node 9 5 2 4 4 7 2 2 8 8 2 1 8 1 1 5 5 7 7 3 Scan arcs out of node 9, one at a time 1 9 9 9 3 3 6 6 6 6 4 9 6 LIST 9 Breadth first search animation

Breadth first search animation Delete node 9 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 Delete node 9 from LIST 9 9 9 9 3 3 6 6 6 6 4 9 6 LIST 9 Breadth first search animation

Breadth first search animation THE END Breadth first search animation

15.082J / 6.855J / ESD.78J Network Optimization MITOpenCourseWare http://ocw.mit.edu 15.082J / 6.855J / ESD.78J Network Optimization Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.