specialized routing problems

8/8/2019 specialized routing problems

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Specialized routing problems

ECE 256A 1

ECE 256a

Malgorzata Marek-Sadowska

References

T. Yoshimura, and E.S. Kuh, Efficient Algorithmsfor Channel Routing , IEEE Transactions onComputer-Aided Design, Volume 1, Issue 1, January

1982 Page(s):25 35. Y. Kajitani, Order of Channels for Safe Routing andOptimal Compaction of Routing Area, IEEETransactions on Computer-Aided Design, Volume

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, , J. Reed, A. Sangiovanni-Vincentelli, M. Santomauro;

A New Symbolic Channel Router: YACR2 , IEEETransactions on Computer-Aided Design, Volume4, Issue 3, July 1985 Page(s):208 219

R.L. Rivest, C.M. Fiduccia, A "Greedy" ChannelRouter, Design Automation Conference, 14-16 June1982 Page(s):418 - 424 .

Specialized routing problem2 2 2 2 21 4

4

h

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Fixed terminals on 2 parallel boundaries.

Movable terminals on the other two boundaries

(sides). 2 layers of metal for wiring. Goal :

connect all nets such that h is minimized, i.e. the

2 boundaries with fixed terminals are as close as

possible.

DESIGN RULES

A. Signal nets

each layer has

its design rules Vccw

Hcc

H1

H2

c

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B. Power nets have also a minimum wire widthon a layer specified.

C. Other nets may have their design rulesdifferent from the other nets.

In theory: We need to connect all terminals,such that all nets are connected and designrules are fulfilled. Minimize height !

In practice : Various additional requirementscaused by

* electrical and timing constraints

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(e.g. max length of overlap on different layers,layer preference, #via per net , etc.)

* constraints due to layout verifiers used incompanies

(only horizontal and vertical wires, griddedrouting, strictly one directional routing onlayers, etc)

The simplest 2 layer routing between 2boundaries of fixed terminals can beformulated when the real problem isabstracted as follows:

* the fixed terminals are at gridded positions ;

* via - via, via - line and line - line design rules

are replaced by their worst case combination -

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orizonta wires are p ace on trac s;

* strictly horizontal/vertical layering isassumed

* no overlap between wires on different layersis allowed.


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Channel Routing

Given a rectangular channel with terminalslocated on both sides, and a set of nets, placethe nets in the channel to minimize its width.

Formulation:Assume uniform net width : track.

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* L1 for horizontal nets

* L2 for vertical connections.

Represent each net segment as an interval,

indicating the terminal connections (or ).

Interval Graph, IG(V, E)

V = {net segments}

E = horizontal relations between the nets:

(vi, vj) E iff nets ni, nj overlap.

The density of IG (max clique size):Channel density: d dmax

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Finding max clique size is NP-complete!

1

42

3

1

3 4

2

The Left Edge Algorithm

1. Sort the intervals Ii in ascending order bytheir left edge coordinates, li. Let I1 be theinterval in the top of the list.

2. Start a new track.

3. Assign I1 to a current track.

Set x = r ri ht ed e coordinate of I .

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max

Remove I1 from the list.

4. Find first interval Ii whose li > xmax.

If found, set I1 = Ii and go to 3.

Otherwise go to 2.

5. Continue until all intervals are placed.

Example1 2

6

43

51

24

3

5

6

Nets to be routed

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Final placement on nets

4 3

1

5 2

6

Problem: vertical constraints

Vertical Constraint Graph, VG(V,E)

V = {net segments}

1

2

1

2

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: re a ons e ween e ne s, vi, vj

iff nets ni, nj have common vertical terminalposition.

Length of the longest path in VG = vmax.

Channel height : d Max(dmax, vmax)

Objective:

Find the routing which minimizes the number

of tracks and satisfies the vertical constraints.

NP- complete!

Can we use the Left Edge Algorithm?

Greedy.

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p mum, no ver ca cons ra n s areimposed.

Sub-optimum, if VG is acyclic.

No solution, if VG is cyclic (doglegs needed).


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Sub-optimality of Constrained Left Edge (CLE)Algorithm

12

3

Intervals sorted

21

3

VerticalConstraint ra h

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1

2

3Solution with Left Edge algorithm

1

2

3 Optimum solution

Breaking vertical constraints with doglegs

1

2

1

2

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1a2

1b

1

12

2

dogleg

Efficient channel routing technique

Modification of the Left Edge Algorithm to

account for vertical constraints [Yos 82,84]

Assign weight wi to net ni as a function of

1. net segment length

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. onges pa eng o

3. local density of the zone to which n i belongs

Net merging: among the nets that fit in a given

track, find a set which maximizes cost function.

Zone representation for horizontal segments

S(i) - the set of nets whose horizontal segments

intersect column i. Horizontal segments of

distinct nets must not overlap => horizontal

segments of any two nets in S(i) can not be

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placed on the same horizontal track. Only

maximal S(i) need to be considered. These are

zones.

MERGING OF NETS1 2 3 4 5 6 7 8 109 11 12

3

1 6 9

2

7

4

5 8 10

7 1

3 2

64

5

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3 8

7

6

2

95

8

10

9

7

VGHG

1 2 3 4 5

1 7

8

9

10

2

3

4

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5 6

zone representation


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Solution from the left edge algorithm:1 2 3 4 5 6 7 8 9 10 11 12

1

5

38

4

6

7

10

92

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xamp e, or w c e -e ge a gor m oesnot produce good results:

1

2

3

1

2

3

2

1 3

zone representation

2

1

3

2

1 3

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LE algorithm Optimum solution

Observation : left - edge algorithm does not look at

the longest path in vertical constraints graph.

Considering longest path reduction is not all !

Example:

21

3

4 5

1 2

3 4

1 2

1 2 3

3

4

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5vertical constraints

5

4

1 2

3

5

4

1

2

3

5

Algorithm

1. Construct the vertical constraint graph and the zonerepresentation. N = set of all nets, T (track count) = 1.

2. While N= O do

3. No = nets with no ancestors in VCG

4. Find Na No such that :

(a) no two nets in Na have horizontal segments overlap

b w = max, where w are wei hts assi ned to net

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n isegments.

5. Place all nets in Na on track T, N = N - Na6. Update the vertical constraint graph VCG and zone

representation.

7. T = T + 1

8. end

n Na

Weight assignment to unplaced nets.

Weights depend on :

* longest path through the net,

* horizontal segment length

* local density of the zones the net belongs to.

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a can e oun rom a rec e or zon a

compatibility graph Nodes - nets, weights of the

nodes = weights of the net segments do not overlap,

from (segment on the left) - to (segment on the

right) Longest path in this graph = Na.

Example

2

1

3

4

6

5

3

4

5

6

2

22

L

2

1R

longest path

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1

w weight


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Building Block Layout Systems

* Blocks differ in size and shape

* Difficulties for CAD tools are caused by:

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rregu ar y o e rou ng area

Ability of blocks to move

2 approaches to routing:

* Divide the routing region into smaller areas and routethem in as small area as possible.

* Route the layout such that blocks can not move(routing too loose or design rules not fulfilled) andcompact/decompact the result.

Problems

I - st approach :

* How to define routing regions?

* How to order routing regions?

* How to update global routing after placementadjustments?

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- n approac :

* How to manage efficiently the size ofdatabase since compaction is done afterdetailed routing has been completed?

* How to schedule compaction steps?

* jog insertion heuristics.

Channel Definition & Ordering

PROBLEM

Carve up routing area into smaller regions - to be

subsequently routed by channel or switch box

routers

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GOALS

* Handle placements of macro cells with anyrectilinear shapes

* Handle any placement including those that arenot in a slicing structure

ROUTING REGION DEFINITIONAND ORDERING

Strai ht Channel

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Routable Channel: when the channel is beingrouted, its width can be expanded orcontracted without destroying the previouslyrouted channels.

Feasible routing order - A routing order

following which all unrouted regions areroutable

-

1

4 3

2

12

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non - feasible order feasible order

Channel Requirements

Lateral Rigidity Pin Definition

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A

B

T Intersection

A

B

Order Dependency


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Slicing StructureA B

C

D

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A

D C

B

Slicing Structure

1 4

2

3

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1

42

3

Cyclic Channel Order Constraint

D

A

B

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C

A

B D

C

L - Shaped Channel Routing Scheme

D

A

B

C1

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C2 A

B-C2 D

C1

L - Shaped Channel Routing Scheme

3

2

1

4

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Topological channel definition 3

2

1

4

Geometrical channel definition

Corner dependencies

C1 vertically depends on C2C horizontall de ends on C

C3

C2

C1C5

C4

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C3 vertically depends on C4C5 horizontally depends on C4C4 is totally independent

There may not exist a totally independent corner.

Always there is either a vertically or horizontally

independent corner.


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[13] K.J.Supowit, E.A. Slutz, Placement Algorithms forcustom VLSI; DAC83.

Channel model : A set of horizontal and vertical segmentswhich meet only at Y - interaction and partition a planeinto rectangles.

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Theorem 1 : Let M = {c0, c1,..cn-1} be a channel model.

G(M) has a cycle G(M) has a cycle of length 4

Theorem 2 : If M is a channel model then G(M) is acyclic M is completely bisectable.

specialized routing problems

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