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EE5900 Robust VLSI Computer-Aided Design

VLSI Channel Routing

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Objectives

• Definition of VLSI channel routing problem• How to perform channel routing for width optimization• Lower bound proof for channel routing• Understand that channel routing problem is difficult to

solve

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Routing Problem

Routing to reduce the area

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Metal layer 1

Via

Routing Anatomy

Topview

3Dview

Metal layer 2

Metal layer 3

Sym

bolic

Layou

t

©Bazargan

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Routing Grid

Horizontal Routing Track

Vertical Routing Track

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Channel Routing Terminology

Upper boundaryUpper boundary

Lower boundaryLower boundary

TracksTracks

Terminals (Gate Pins)Terminals (Gate Pins)ViaVia

Width Width (# of Horizontal Routing Tracks)(# of Horizontal Routing Tracks)

Assume that there are only one horizontal layer and only one vertical layer, i.e., no overlap among horizontal wires and no

overlap among vertical wires will be allowed.

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Channel Routing Problem - I

• Input: – Two vectors of the same length to represent the pins on two

sides of the channel.– One horizontal layer and one vertical layer.

• Output:– Connect pins of the same net together such that there is no

overlap among horizontal wires and there is no overlap among vertical wires.

– Minimize the channel width.

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Channel Routing Problem - II

00 11 22 22 00 33 00 44

11 22 00 33 33 44 44 00

Example: (01220304) (12033440)where 0 = no terminalRoute all the pins with the same index

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A Channel Routing Example

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

2 3 5 3 5 2 6 8 9 8 7 9

How good is it?

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A Simpler Example - I

Is this routing with the minimum width?

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A Simpler Example - II

Is this routing with the minimum width?

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Lower Bound on Channel Width00 11 66 11 22 33 55

66 33 55 44 00 22 44

00 11 66 11 22 33 55

66 33 55 44 00 22 44

11 2233

55 4466

LocalLocaldensitydensity 11 33 44 44 44 44 22

Channel density =Channel density =Maximum local densityMaximum local density

Lower bound = 4Lower bound = 4

Lower bound on channel width = Channel density

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Exercise

• Use minimum number of tracks to route the following nets. Is your result the best possible one?

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Lower Bound Always Achievable?

• Is the channel routing lower bound always achievable for any channel routing problem?

11 22 11

22 11 22

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A More Complex Example

# columns =174, # nets=72, density =19

Routing result:number of tracks=20

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Realistic Design

From DAC Knowledge CenterDifferent colors refer to different wire densities. Red color means large

congestion.

# routes actually on a track

max # routes allowed on a track

Congestion=

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Summary

• Definition of VLSI channel routing problem• Channel routing for width optimization• Lower bound for channel routing

– Local Density and Channel Density

• Lower bound is not always achievable• We will discuss about the channel routing computer-

aided design algorithm in the next lecture