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15.082 and 6.855J

15.082 and 6.855J. Label Correcting Algorithm. An Example. . . 2. 4. 2. 3. 3. 3. 1. . . -2. 6. 1. 5. 7. 0. 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).

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15.082 and 6.855J

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  1. 15.082 and 6.855J Label Correcting Algorithm

  2. An Example   2 4 2 3 3 3 1   -2 6 1 5 7 0 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.

  3. An Example 2  3  3 3 3 1 -2 6 0   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.

  4. An Example 2  3  3 3 3 1 -2 6 0  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.

  5. An Example 2  3  3 3 3 1 -2 6 0 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.

  6. An Example 2  5  3 3 3 3 1 -2 6 0 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.

  7. An Example 2 5  3  3 3 3 1 -2 6 0  4 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.

  8. An Example 2 5  3  3 3 3 1 -2 6 0 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.

  9. An Example 2 5  3  3 3 3 1 -2 6 0 6  4  Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 3  2  6 Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

  10. An Example 2 5  3  3 3 3 1 -2 6 0  6 4 9  Generic Step 2 3 4 3 An arc (i,j) is violating if d(j) > d(i) + cij. -4 3 2   6 Pick a violating arc (i,j) and replace d(j) by d(i) + cij.

  11. An Example 2 5  3  3 3 3 1 -2 6 0 4  6  9 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. No arc is violating We now show the predecessor arcs. The distance labels are optimal

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