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NEMO: A New I mplicit NEMO: A New I mplicit Connection Graph- -Based Based Gridless Gridless Connection Graph Router with Multi- -Layer Planes Layer Planes Router with Multi and Pseudo- -Tile Propagation Tile Propagation and Pseudo

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NEMO: A New I mplicit NEMO: A New I mplicit Connection Graph Connection Graph-

  • Based

Based Gridless Gridless Router with Multi Router with Multi-

  • Layer Planes

Layer Planes and Pseudo and Pseudo-

  • Tile Propagation

Tile Propagation

Hsin-Yu Chen Yih Yih-

  • Lang Li

Lang Li Zhi Zhi-

  • Da

Da Lin Lin

Computer Science Departm Computer Science Department, ent, Faraday Tech. Corp. National Chiao Faraday Tech. Corp. National Chiao-

  • Tung University (NCTU)

Tung University (NCTU)

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Introduction New Implicit Connection Graph-Based Router (NEMO) General-Purpose Routing Experimental Results Conclusion Introduction

Outline Outline

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Why Why Gridless Gridless Routing ? Routing ?

  • Variable

Variable-

  • width and variable

width and variable-

  • space routing

space routing becomes inevitable for modern designs becomes inevitable for modern designs

– – Wide space and fat wire for crosstalk and delay

Wide space and fat wire for crosstalk and delay

  • ptimization
  • ptimization
  • Gridless

Gridless routers are more flexible for variable routers are more flexible for variable-

  • rule

rule routing than grid routing than grid-

  • based routers

based routers

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rule Half width rule separation

Basic Basic Concept Concept

Zero-width Model Nonzero-width Model

rule Half width rule separation

2 × s + w s w

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I mplicit Connection I mplicit Connection Graph Graph-

  • Based Router

Based Router

Fast routing graph construction

B A C D 0 1 2 ………………………………….. 16 ...…………………… 11 1 2 Four slices I3 I2 B I3 I1 A

R1 R2 R3 R4

R1 R2 C R3 D R4 I1 I2

Efficient query data structure (Slit tree + Interval Tree)

  • J. Cong et al., “An Implicit connection graph maze

Routing Algorithm for ECO routing,” in ISPD99

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I mplicit Connection I mplicit Connection Routing Graph Routing Graph

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Contribution of This Work Contribution of This Work

  • We propose a new implicit connection

We propose a new implicit connection graph graph-

  • based router with pseudo

based router with pseudo-

  • tile

tile extraction and propagation to extraction and propagation to

– – reduce the time required for query

reduce the time required for query

  • perations
  • perations

– – speed up path searching.

speed up path searching.

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Introduction New Implicit Connection Graph-Based Router (NEMO) General-Purpose Routing Experimental Results Conclusion New Implicit Connection Graph-Based Router (NEMO)

Outline Outline

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Features of NEMO Features of NEMO

  • Multi

Multi-

  • Plane Routing Graph

Plane Routing Graph

  • Tile plane but not grid plane

Tile plane but not grid plane

  • Non

Non-

  • zero width wire model

zero width wire model

  • Pseudo Maximum (horizontally or

Pseudo Maximum (horizontally or vertically) Stripped Tile (PMT) Extraction vertically) Stripped Tile (PMT) Extraction and Propagation and Propagation

  • Pseudo Blockage Insertion & Gridline

Pseudo Blockage Insertion & Gridline Reduction Reduction

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Multi Multi-

  • Plane Routing Graph

Plane Routing Graph

: L 1 : L 2 : L 3 An 3-layer routing example L 1 L 2 L 3

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Why Tile, Not Grid Why Tile, Not Grid

Grids on adjacent Layers don’t align L1 L2

L1x(1) L1x(2) L1x(3) L1x L1y(2) L1y(1) L1y(3) L1y(4) L1x(1) L1x(2) L1x(3) L1x(4) L1y(2) L1y(1) L1y(3) L1y(4) L1x(1) L1x(2) L1x(3) L1x(4) L1y(2) L1y(1) L1y(3) L1y(4) L1x(1) L1x(2) L1x(3) L1x(4) L1y(2) L1y(1) L1y(3) L1y(4)

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Non Non-

  • Zero Width Wire Model

Zero Width Wire Model

rule Half width rule separation

Ws Ws

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Multi Multi-

  • Layer Routing

Layer Routing

CA1x CA2x CA1y CA2y

L2y(1) L2y(2) L2y(3) L2y(4) L1x(1) L1x(2) L1x(3) L1x(4) L1y(1) L1y(2) L1y(3) L1y(4) L2x(1) L2x(2) L2x(3) L2x(4)

A

L1x(1) L1x(2) L1x(4) L1x(3) L1y(1) L1y(2) L1y(3) L1y(4)

T(1,1) T(2,1) T(1,2)

Layer 2: T(1,1), T(2,1), T(3,1) T(1,2), T(2,2), T(3,2) Layer 1 Layer 2

T(1,1) T(2,1) T(1,1) T(1,2)

L2x(1) L2x(3) L2y(4) L2x(2) L2y(3) L2y(2) L2x(4) L2y(1)

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Path Search by PMT Path Search by PMT

Maximum horizontally stripped

A B

T1 T2

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PMT Extraction PMT Extraction – – Tile Query Tile Query

: obstacle

L R L R L R

BR BL

C Three Cut lines three internal nodes A B

L R L R L R

LA LC LB

Point query

A

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1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5 5 5 6 7 7 7

P1 P2 P3

X Y Z A B C D

PMT Extraction PMT Extraction – – Merging Merging

P1 P2 P3 P1 P2 P3

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Introduction New Implicit Connection Graph-Based Router (NEMO) General-purpose Routing Experimental Results Conclusion General-purpose Routing

Outline Outline

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Routing Flow Routing Flow

Decompose multi-terminal net routing into multiple 2-pin net routing Decompose multi-terminal net routing into multiple 2-pin net routing Perform congestion-driven global routing Perform congestion-driven global routing Complete point-to-point detailed routing Complete point-to-point detailed routing Rip up and Rerouting Rip up and Rerouting

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S T S T

Pseudo Block I nsertion Pseudo Block I nsertion

: global path : blockage G L O B A L P A T H

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Gridline Reduction Gridline Reduction

S T S T S T S T

Active blockages Idle blockages Global path

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Introduction New Implicit Connection Graph-Based Router (NEMO) Full-Chip Routing Experimental Results Conclusion Experimental Results

Outline Outline

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Experimental Results Experimental Results – – Point Point-

  • to

to-

  • point Routing

point Routing

7320.00 7320.00 × × 7320.00 7320.00 1,018,221 1,018,221 1,649,866 1,649,866 D2 D2 470.00 470.00 × × 455.00 455.00 3,720 3,720 5,106 5,106 D1 D1 Met3 Met3 Met2 Met2 Chip Dimension Chip Dimension x x × × y (um ) y (um ) Rectangles Rectangles Test Case Test Case 9.81 9.81 0.094 0.094 8 8 649.00 649.00 0.922 0.922 8 8 649.00 649.00 TEST5 TEST5 9.41 9.41 0.078 0.078 8 8 527.50 527.50 0.734 0.734 8 8 527.50 527.50 TEST4 TEST4 8.44 8.44 0.063 0.063 12 12 419.50 419.50 0.532 0.532 12 12 419.50 419.50 TEST3 TEST3 10.96 10.96 0.047 0.047 6 6 382.20 382.20 0.515 0.515 6 6 382.20 382.20 TEST2 TEST2 6.6 6.6 0.109 0.109 10 10 539.50 539.50 0.719 0.719 10 10 539.50 539.50 TEST1 TEST1 SU SU Time (s) Time (s) #Via #Via WL ( WL (µ µm) m) Time (s) Time (s) #Via #Via WL ( WL (µ µm) m) NEMO NEMO Cong et al. ISPD99 Cong et al. ISPD99

Table 1. Statistics of the design under the test Table 2. Point-to-point routing results for the circuit D1

9

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4.57 4.57 72 72 180 180 15413.00 15413.00 329 329 180 180 15413.00 15413.00 TEST8 TEST8 12.18 12.18 11 11 410 410 11538.00 11538.00 134 134 410 410 11538.00 11538.00 TEST7 TEST7 13.63 13.63 8 8 374 374 10212.00 10212.00 109 109 374 374 10212.00 10212.00 TEST6 TEST6 6.64 6.64 25 25 490 490 12375.00 12375.00 166 166 458 458 12391.00 12391.00 TEST5 TEST5 11.55 11.55 11 11 446 446 11794.00 11794.00 127 127 446 446 11794.00 11794.00 TEST4 TEST4 16 16 6 6 246 246 8299.00 8299.00 96 96 246 246 8299.00 8299.00 TEST3 TEST3 4.47 4.47 38 38 366 366 9478.00 9478.00 170 170 366 366 9478.00 9478.00 TEST2 TEST2 14.6 14.6 5 5 238 238 4997.00 4997.00 73 73 238 238 4997.00 4997.00 TEST1 TEST1 SU SU Time (s) Time (s) #Via #Via WL ( WL (µ µm) m) Time (s) Time (s) #Via #Via WL ( WL (µ µm) m) NEMO NEMO Cong et al. ISPD99 Cong et al. ISPD99

Experimental Results Experimental Results – – Point Point-

  • to

to-

  • point Routing

point Routing

Table 3. Point-to-point routing results for the circuit D2

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Experimental Results Experimental Results – – General General-

  • Purpose Routing

Purpose Routing

42931 42931 28177 28177 3 3 12950 x 6720 12950 x 6720 S38584 S38584 32344 32344 21035 21035 3 3 11440 x 6190 11440 x 6190 S38417 S38417 12793 12793 8321 8321 3 3 7050 x 3890 7050 x 3890 S15850 S15850 10776 10776 6995 6995 3 3 6600 x 3650 6600 x 3650 S13207 S13207 4260 4260 2774 2774 3 3 4040 x 2250 4040 x 2250 S9234 S9234 4818 4818 3124 3124 3 3 4350 x 2390 4350 x 2390 S5378 S5378 #Pins #Pins #Nets #Nets #Layers #Layers Size ( Size (µ µm m) ) Circuit Circuit

Table 4. Statistics of the benchmark circuits for general-purpose routing

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1 1 0.989 1.26 2.42 34.4

Comp. 6.7e5 146.5 6.6e5 209/174.2

  • 466/171

2535

  • 7086/2599

S38584 4.8e5 55 4.7e5 70.7/58.9

  • 251/92

1945

  • 3560/1306

S38417 2.2e5 15.5 2.2e5 22.7/18.9

  • 107/39

978

  • 1469/539

S15850 1.8e5 10.2 1.8e5 17.9/14.9

  • 85/31

877

  • 1099/403

S13207 5.5e4 2.7 5.4e4 4.3/3.6

  • 23/8

307

  • 355/130

S9234 7.5e4 3.7 7.4e4 5.7/4.8

  • 30/11

517

  • 430/158

S5378 # of F.N. WL

( (µ µm) m)

Time (s) # of F.N. WL

( (µ µm) m)

T/Tn (s) # of F.N. WL

( (µ µm) m)

T/Tn (s) # of F.N. WL

( (µ µm) m)

T/Tn (s) (D) NEMO (C) Multilevel Routing Chen et al. ASP-DAC06 (B) Multilevel Routing Cong et al. TCAD05 (A) Three-Level Routing Cong et al. TCAD05 Circuit (A) And (B) were run on a 440-MHz Sun Ultra-10 with 384MB memory (C) was run on a 1 GHz Sun Blade 2000 with 8 GB memory (D) was run on a 1.2 GHz Sun Blade 2000 with 2 GB memory

Experimental Results Experimental Results – – General General-

  • Purpose Routing

Purpose Routing

Table 5. The comparison of routing results among four gridless routers

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146.5 60180 6.7e5 1953/1628 61053 7.7e5 S38584 55 43193 4.8e5 899/749 43551 5.9e5 S38417 15.5 17260 2.2e5 538/448 17334 2.4e5 S15850 10.2 14865 1.8e5 106/88 14938 2.2e5 S13207 2.7 5818 5.5e4 26/22 6287 6.0e4 S9234 3.7 7045 7.5e4 35/29 7163 8.2e4 S5378

# of F.N.

Time (s) #Vias

WL

(µm)

# of F.N.

T/Tn (s) #Vias

WL

(µm) (B) NEMO (A) Multilevel Router without antenna avoidance Ho et al. ISPD04 Circuit (B) was run on a 1GHz Sun Blade 2000 with 1 GB memory Table 6. The comparison of routing results between a multi-level grid-based router and NEMO

Experimental Results Experimental Results – – General General-

  • Purpose Routing

Purpose Routing

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Conclusions Conclusions

  • We propose a new implicit connection

We propose a new implicit connection graph graph-

  • based router with

based router with

– – Efficient PMT extraction,

Efficient PMT extraction,

– – PMT propagation, and

PMT propagation, and

– – Simplified connection graph

Simplified connection graph

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THANK YOU THANK YOU VERY MUCH VERY MUCH