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Dr.Abhijit RAsatiEEEDepartment,BITS,Pilani

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Routing:

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Routing problem:

Size Complexity:Shape Complexity: m ng omp ex y:

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Maze routing algorithm:

(1) Lee Algorithm:BFS: begins at root node and explores all neighboring nodes

2 Souk u 's Al orithm: Im rovement over basic Lee al orithm

(3) Hadlock's Algorithm: Improvement over basic Lee algorithm

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Routing Constraints

Number of routing layersArea minimization eome r ca

Timing

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Finding coarse grid capacity:

L=Number of layers

h=Height of channelW=Wire width

=

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Let,

L=2 h=18 W=3 S=3 then

channel capacity=(218)/(3+3)

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Global Routing for Gate Arrays:

Constraints:

Minimization of wire lengthsMinimization of path lengths

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Global routing for Standard Cell:

Global Routing used to-

Minimize channel heightdo not have predetermined capacity

Assi nment of feed-throu h

predetermined capacitiesHigh Performance (Minimize wire and path length)

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Lees Maze Algorithm:

Consider a sin le 2 oint net in a lane that ma contain obstaclesOne point source the other target

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Define a fine grid:

Grid overlaid on laneEach grid square is where one wire can crossSize of the grid squares is the minimum wire pitch

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Wave propagation Phase:

Be in at source, find cells at distance '1',Find cells at distance 2The ith wave front always contains all cells at Manhattan distance i

Propagate the wave till target cell also gets labeled.

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Backtracking Phase:

Go back along path in grid

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Reducing the number of bends?

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Length=10

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Note: In many practical situations the shortest path may not be more

.

Label clearance Phase:

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Running time is proportional to the number of cells searched in filling

.

Speed up of filling phase or wave propagation phase Lee algorithm can

e o a ne us ng:

Starting point selection.

Double fan out.

Framing: Artificial boundary

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Starting point selection:

Double fan out:

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Framing: Artificial boundary

The frame can be 10-20% larger than the bounding box containingS and T.

.

Total number of bits=12

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Ackers coding scheme:

Reduces the memory requirement.

Fillin se uences that reduce memor re uirement. a Se uence

1,2,3, 1,2,3. . . . (b) Sequence 1,1, 2,2, 1,1, 2,2 . . . .

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For sequence 1,2,3, 1,2,3. . . .:

{1, 2, 3, blocked, empty}= 3-bits

For se uence 1 1 2 2 1 1 2 2 . . . .:

{1, 2, blocked, empty}= 2-bits

, .

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Weighted Lee Algorithm:

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TerminalsTerminals

ViaVia

Upper boundaryUpper boundary

TracksTracks DoglegDogleg

Lower boundaryLower boundary

TrunksTrunks BranchesBranches

The splitting of horizontal segments of a net is called doglegging.

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Basic Left-Edge Algorithm (Unconstrained Left Edge Algorithm):

Segments of nets to be connected are sorted in the increasing order oftheir left end points from the left edge of the channel.

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Left edge Sequence: 3,1,2,4

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Sequence: 6,1,3,5,4,2

Trunk part of nets overlaps (cant be placed on some track).

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Left edge Sequence: 6,1,3,5,4,2

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Vertical constraint:

If a net i has a in at the to in a column then in on the

bottom of channel in the same column introduces an edge (i,j).

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Constrained Left Edge Algorithm:

Sequence: 6,1,3,5,4,2

Segments corresponding to a net can be placed in a track only if itsescen en s ave a rea y een ass gne .

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Left edge Sequence: 6,1,3,5,4,2

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Dogleg Router:

Eight different routing sequences are:

. op e o om r g . op e o om e

3. top right bottom right 4. top right bottom left5. bottom left top left 6. bottom left top right

7. bottom right top left 8. bottom right top right

t l ft b tt i ht

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top left bottom right

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Deutch Dogleg Algorithm:

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(a) Solution using constrained left edge algorithm:

a=

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(b) Solution using Deutch dogleg algorithm:

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o. of tracks without spliting = 4

No. of vias without spliting = 10No. of tracks with spliting = 3 =.

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Standard cell Over the Cell Routing (OTC):

.The channels have almost disappeared giving rise to channel-lessstandard cell designs.

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Cell Models

Based on the locations of the terminals there are four major classes of

cell models :

Boundary Terminal Models (BTM)

The Center Terminal Models(CTM)The Middle Terminal Model MTMThe Target Based Cell Mode(TBC)

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Boundary Terminal Models (BTM):

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Centre Terminal Models (CTM):

Th Middl T i l M d l (MTM)

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The Middle Terminal Model (MTM):

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The Target Based Cell Model (TBC):

- - .

T l th ll t

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Two layer over the cell routers:

Following is example of OTC algorithm using CTM cell model.

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River routing:

.

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Pins are located along a boundary

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Pins are located along a boundary.

Starting terminal AssignmentNet orderingPath SearchingCorner Minimization

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Startin terminal Assi nment:

Net ordering:Path Searching:

Starting terminal Assignment:

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Starting terminal Assignment:

et ordering:

Switchbox Routing:

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Switchbox Routing: