1. Optimal Non-Manhattan Bubble Sort Channel Router
Sean Pieper ECE556 Final Project

2. Non-Manhattan Routing
can use +/- 45 degree paths
“X” routing requires one track and no extra columns
No need for VCG or HCG
Use Vertical and Horizontal Constraint Graphs (VCG and HCG)
If VCG has a cycle, need to add extra columns and rows.

3. How to cash in:
Constrain problem to two-terminal nets
Each net crosses the channel
Rename terminals so that top is numbered in order
Bottom can now be viewed as a permutation of the top
58324
43258
12345
53412
At each track:
swap adjacent wires that are out of order with respect to each other
For N terminals, this router requires N columns and at most N tracks

4. Better idea: Sort Routing
Swap router only allows wires to move one column per track
We have horizontal tracks available, so this is an artificial constraint
Bubble sort will move tracks horizontally

5. Optimize it: At each new track, can sort left or right
Left sort moves tracks left rapidly, right sort moves tracks right
Previous example would take 9 layers with only right sort
Want to use optimal combination of left and right sort steps

6. Breadth first search:
Ordering of left and right sorts does not matter:
Full tree has redundant nodes
Collapse redundant nodes to get DAG
Remove redundant paths from DAG
Order dependent tree
DAG
Vector of Vectors

7. Code flow:
Parse input file: use hashtable to accelerate renaming of pins
All leaves
generated
Expand main
vector
Expand
Left sub-vectors
Not sorted
Perform one right sort step
Perform one left sort step
Check for
sorted leaf
Done
When a sorted leaf is found, the number of left and right steps that generated it is returned. This uniquely identifies the sequence of intermediate routing steps
Generate
ASCII art
of routing

8. Sample Output:
| | | | | / / | | | | | | | |
| | | | o---o | | | | | | | | 1
| | | | / / | | | | | | | | |
| | | | | | | | | / / | \ / |
| | | o---o | | o---o | \ | 2
| | | / / | | | / / | | / \ |
| / / | | | | | | | | | | / |
o o | | o---o | o---o | 3
/ / / / | | | / / | | / / | |
\ \ \ \ \ \ \ | | \ \ | \ \ |
o o | o---o o---o 4
| \ \ \ \ \ \ \ | | \ \ | \ \

9. Performance Results:

10. Questions?