15.082J & 6.855J & ESD.78J Visualizations

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15.082J & 6.855J & ESD.78J Visualizations Label Correcting Algorithm Obtain a network, and use the same network to illustrate the shortest path problem for communication networks, 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.)

An Example ∞ ∞ 4 2 ∞ ∞ 1 5 7 Initialize d(1) := 0; d(j) := ∞ for j ≠ 1 3 3 3 1 ∞ ∞ -2 6 1 5 7 Initialize 2 3 4 3 d(1) := 0; d(j) := ∞ for j ≠ 1 -4 3 6 ∞ ∞ In next slides: the number inside the node will be d(j). Violating arcs will be in thick lines.

An arc (i,j) is violating if d(j) > d(i) + cij. ∞ ∞ 2 ∞ 3 ∞ 3 3 3 1 -2 6 ∞ ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 ∞ ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. ∞ ∞ 2 ∞ 3 3 3 3 1 -2 6 ∞ 6 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 ∞ ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. ∞ 3 ∞ 2 ∞ 3 3 3 3 1 -2 6 6 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 ∞ 3 ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 3 ∞ 2 5 ∞ 3 3 3 3 1 -2 6 6 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 3 ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 3 ∞ 2 5 3 3 3 3 1 -2 6 6 4 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 3 ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 3 6 ∞ 2 5 3 3 3 3 1 -2 6 6 4 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 3 6 ∞ Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 2 3 ∞ 6 5 3 3 3 3 1 -2 6 6 4 ∞ Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 2 3 ∞ 6 Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 2 6 5 3 3 3 3 1 -2 6 4 ∞ 9 Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 2 6 Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

An arc (i,j) is violating if d(j) > d(i) + cij. 2 6 5 3 3 3 3 1 -2 6 4 9 Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 2 6 Pick a violating arc (i,j) and replace d(j) by d(i) + cij. No arc is violating We now show the predecessor arcs. The distance labels are optimal

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.