Multi-Layer Channel Routing Complexity and

Algorithm

Rajat K. Pal

Chapter- 4A Framework for Track Assignment

Presented by:

Abu Sayed Chowdhury

0409052008

Multi-Layer Routing (Extensions of the TAH Framework)

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

Pre-requisite (Contd.)

Net

Cells have rectangular shapes with terminals located on their border.

A set of terminals that must be electronicallyconnected together, constitute a net.

Terminals of the same net are given the same integer level

C

EA D

B

F

C

EA D

B

F

VLSI Layout

Pre-requisite (Contd.)

Net

Channel Routing Terminology

Upper boundaryUpper boundary

Lower boundaryLower boundary

TracksTracks

TerminalsTerminalsViaVia

TrunksTrunks BranchesBranches

DoglegDogleg

Routing Layer Models

HV modelHV modelVH modelVH model

HVH modelHVH modelVHV modelVHV model

Layer 1Layer 1Layer 2Layer 2Layer 3Layer 3ViaVia

1 layer1 layer

2 layers2 layers

3 layers3 layers

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

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.

I2

I7

I5

I4

I1

I3

I6

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

I8

I9

I10

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

maxd

I2

I7

I5

I4

I1

I3

I6

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

I8

I9

I10

1 4 6 7 8

10

2953

VCG

I4

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

I10

1 6 7 8

2953

VCG

Track 1

I7

I1

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

68

2953

VCG

Track 2

I5

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

8

23

VCG

Track 3

I6 I9

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

3

VCG

Track 4

I2 I8

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

3

VCG

Track 4

I2 I8

0 1 4 5 1 6 7 0 4 9 10 0 10

2 3 5 2 6 8 9 8 7 0 93 5

Track 5

I3

Finally using TAH

A Two Layer No Dog-leg routing solution for Ex.2 using TAH

Thanks to All