MultiLayer Channel Routing Complexity and Algorithm

1
Multi-Layer Channel Routing Complexity and
Algorithm

• Rajat K. Pal

2
Chapter- 4A Framework for Track Assignment
Multi-Layer Routing (Extensions of the TAH
Framework)

• Presented by
• Abu Sayed Chowdhury
• 0409052008

3
Pre-requisite

• Channel
• A channel is a horizontal routing area with
  fixed pins on the top and bottom
• TAH Framework
• Algorithm for computing reduced wire length
  channel routing solutions using a purely graph
  theoretic framework, TAH (Track Assignment
  Heuristic) that was designed for computing
  minimum area routing solutions

4
Pre-requisite (Contd.)
Net
Cells have rectangular shapes with terminals
located on their border.
A set of terminals that must be
electronically connected together, constitute a
net.
Terminals of the same net are given the same
integer level
5
Pre-requisite (Contd.)
D
D
A
A
E
E
C
C
B
B
F
F
VLSI Layout
Net
6
Channel Routing Terminology
Terminals
Via
Upper boundary
Tracks
Dogleg
Lower boundary
Trunks
Branches
7
Routing Layer Models
1 layer
HV model
VH model
2 layers
Layer 1
Layer 2
Layer 3
Via
HVH model
VHV model
3 layers
8

• An example channel instance of ten nets
• Intervals of the nets are placed in five
  different tracks
• The length of the channel (i.e., the number of
  columns) is 15
• Arrows indicate that the terminals to be
  connected, either on the top or at the bottom, to
  complete the required interconnection of all the
  nets present in the channel

9
TAH Basics

• The Algorithm TAH assigns intervals to tracks
  from top to bottom.
• In the first iteration the algorithm assigns a
  set of non-overlapping intervals to the top most
  track. Then it delete the nets corresponding to
  these intervals from the channel.
• In the second iteration it assigns a set of
  non-overlapping intervals to the second track.
• The iterative process continues till all the nets
  are assigned to tracks in the channel.

10
(No Transcript)
11
10
0
1
4
1
4
9
0
5
6
7
0
10
I10
I1
I4
I9
I5
I6
I7
I3
I8
I2
2
3
2
9
7
0
3
5
5
6
8
8
9

• The Channel contains total 10 nets
• Density of this channel is ( ) is 5
• Intervals of nets 1, 4, 5, 3, and 2 are
  overlapping to
• each other, and form a clique

12
10
0
1
4
1
4
9
0
5
6
7
0
10
I10
I1
I4
I9
I5
I6
I7
I3
I8
I2
2
3
2
9
7
0
3
5
5
6
8
8
9
8
7
6
VCG
1
4
10
9
2
5
3
13
Track 1
10
0
1
4
1
4
9
0
5
6
7
0
10
I4
I10
2
3
2
9
7
0
3
5
5
6
8
8
9
8
7
6
VCG
1
9
2
5
3
14
Track 2
10
0
1
4
1
4
9
0
5
6
7
0
10
I1
I7
2
3
2
9
7
0
3
5
5
6
8
8
9
8
6
VCG
9
2
5
3
15
Track 3
10
0
1
4
1
4
9
0
5
6
7
0
10
I5
I6
I9
2
3
2
9
7
0
3
5
5
6
8
8
9
8
VCG
2
3
16
Track 4
10
0
1
4
1
4
9
0
5
6
7
0
10
I2
I8
2
3
2
9
7
0
3
5
5
6
8
8
9
VCG
3
17
Track 4
10
0
1
4
1
4
9
0
5
6
7
0
10
I2
I8
2
3
2
9
7
0
3
5
5
6
8
8
9
VCG
3
18
Track 5
10
0
1
4
1
4
9
0
5
6
7
0
10
I3
2
3
2
9
7
0
3
5
5
6
8
8
9
19
Finally using TAH
20
A Two Layer No Dog-leg routing solution for Ex.2
using TAH
21

• Thanks to All