1. An Introduction to Channel Routing
曾奕倫
元智大學資訊工程系
2008/07/11

2. A Channel Routing Problem

3. A Channel Routing Problem (cont’d)

4. A Channel Routing Problem (cont’d)

5. A Solution to the Channel Routing Problem

6. A Solution to the Channel Routing Problem (in VLSI Physical Design)
Different colors represent different layers.

7. A Solution to the Channel Routing Problem (cont’d)
Minimizing the number of tracks means minimizing the routing area.

8. A Channel Routing Problem

9. A Channel Routing Problem (cont’d)

10. Description of a Channel Routing Problem
Columns:
Nets: A B C D E F
Top_Row: C NULL F E B NULL A
Bottom_Row: A NULL NULL B NULL B C
Left_Nets: A D F
Right_Nets: D E
(The Input to Your Channel Router)

11. Vertical Constraint Graph
At column 1, the horizontal segment of net C must be placed above the horizontal segment of net A.

12. Vertical Constraint Graph (cont’d)
At column 1, the horizontal segment of net C must be placed above the horizontal segment of net A.

13. Vertical Constraint Graph (cont’d)
At column 4, the horizontal segment of net E must be placed above the horizontal segment of net B.

14. Vertical Constraint Graph (cont’d)
At column 7, the horizontal segment of net D must be placed above the horizontal segment of net C.
VCG

15. The Left-Edge Algorithm
Proposed by Hashimoto and Stevens in 1971
Regarded as the first channel routing algorithm
Can be used in solving Channel Routing Problems
Originally used in PCB design
Can be applied on VLSI physical design
Requires building the Vertical Constraint Graph (VCG) for a channel routing problem

16. The Left-Edge Algorithm (cont’d) Step 1: Build VCG

17. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Consider horizontal segments of N1, N4, and N10
(the nets that do not have ancestors)

18. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
N1 has the smallest x coordinate
N1 and N4 cannot be placed on the same track
N1 and N10 can be placed on the same track
Place N1 and N10 on the highest track

19. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
N1 has the smallest x coordinate
N1 and N4 cannot be placed on the same track
N1 and N10 can be placed on the same track
Place N1 and N10 on the highest track

20. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Update the VCG
(remove N1 and N10 from the VCG)

21. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Update the VCG
(remove N1 and N10 from the VCG)

22. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Consider horizontal segments of N4 and N7
(the nets that do not have ancestors)

23. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Consider horizontal segments of N4 and N7
(the nets that do not have ancestors)

24. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Consider horizontal segments of N4 and N7
(the nets that do not have ancestors)
N4 has the smallest x coordinate
N4 and N7 cannot be placed on the same track
Place N4 on the second highest track

25. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Consider horizontal segments of N4 and N7
(the nets that do not have ancestors)
N4 has the smallest x coordinate
N4 and N7 cannot be placed on the same track
Place N4 on the second highest track

26. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Update the VCG
(remove N4 from the VCG)

27. The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments
Update the VCG
(remove N4 from the VCG)
Repeat the placement iterations …

28. The Left-Edge Algorithm (cont’d) - Result of the Example

29. The Left-Edge Algorithm (cont’d) - Result of the Example
(The Output of Your Channel Router)

30. The Left-Edge Algorithm (summary)
Step 1: Build the Vertical Constraint Graph (VCG) for the input channel routing problem
Step 2: Place horizontal segments (choose nets (1) that do not have ancestors in the VCG and (2) whose horizontal segments do not overlap) and update the VCG
Step 3: Repeat Step 2 until all the horizontal segments have been placed

31. A Channel Routing Problem
Dogleg Channel Routing

32. A Channel Routing Problem (cont’d)
Loop
VCG
The Left-Edge Algorithm cannot deal with a channel routing problem whose VCG contains loops.

33. Channel Density Channel Density = 5
At least 5 tracks are required in order to solve this channel routing problem (with or without doglegs).

34. To-Do List Choose a Programming Language
Implement a Graphical User Interface (GUI) for displaying (1) a channel routing problem (the input) and (2) its solution (the output)
Implement the Left-Edge Algorithm
Build the VCG (step 1)
Data Structure (Adjacency List)
How to find nets that have no ancestors in the VCG
How to delete nets from the VCG
Placement of horizontal segments (step 2)
How to check the existence of loops in a VCG