# 15.082 and 6.855J - PowerPoint PPT Presentation

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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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## 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).

Violating arcs will be in thick lines.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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