porosity aware buffered steiner tree construction c. alpert g. gandham s. quay ibm corp m. hrkic...
TRANSCRIPT
Porosity Aware Buffered Steiner Tree Construction
C. Alpert
G. Gandham
S. Quay
IBM Corp
M. Hrkic
Univ Illinois ChicagoJ. Hu
Texas A&M Univ
Outline
• Introduction and Previous work
• Problem formulation
• Algorithm
• Experimental results
• Conclusion
Buffer Insertion• Improve timing
– Drive long wire– Shield load from critical
path
• Van Ginneken’s Algorithm– Given tree topology
fixed– Find optimal solution at
fast speed
Slack
Slack
73
-23
24
33
If There Are Big Blockages
Previous Works
• Simultaneous tree construction and buffer insertion– Buffer blockage driven
• Recursively Merging and Embedding [Cong and Yuan, DAC 00]• Graph-based[Tang, et al., ICCAD 01]
– General purpose• SP-Tree [Hrkic and Lillis, ISPD 02]
– Excellent solution quality– High complexity
• Sequential tree construction + buffer insertion– Adaptive blockage avoidance [Hu, et al., ISPD 02]– Very good solution quality– Practical computation speed
If There Are Many Small Blockages
Porosity Has to Be Considered
• Handling small blockages will slow down computation
• Buffers in dense region may be spiraled away
• No previous work handles porosity directly
Express Porosity through Tile Graph
• For a tile g• A(g): tile area• a(g): usage area• d(g) = a(g)/A(g)• Porosity cost is
d2(g), if a buffer is placed in g
Problem Formulation
Porosity-aware Buffered Steiner Tree Problem: • Given
– A net N = {v0, v1, …, vn} – Load capacitance c(vi) and required arrival time q(vi) – Tile graph G(VG, EG)
• Construct a Steiner tree T(V,E), such that– Required arrival time q(vi) are satisfied– Total porosity cost is minimized
Observation• Easy to deal with node-to-node path
– Congestion can be avoided by rerouting without affecting timing
• Hard to deal with Steiner nodes– Moving Steiner nodes may degrade timing
Basic Strategy
• Construct a timing driven Steiner tree regardless porosity
• Adjust Steiner nodes simultaneously with length-based buffer insertion– Adjustment range need to be restrained– A Steiner node is moved only when buffer
is needed there
Length-based Buffer Insertion
• Simple buffering following rule of thumb– Capacitance load of driver/buffer ≤ bound L
• Dynamic programming based• Candidate solutions are propagated bottom-
up• Solution is characterized by load capacitance
and porosity cost• A solution with greater load and cost will be
pruned
L=2
Plate: Adjustment Range
Plate-based Adjustment
• Integrate Steiner node adjustment with length-based buffer insertion
• Solutions are propagated to and merged at each tile of plate
• Merged solutions at each tile are further propagated toward root
• Alternative topologies are generated • A candidate topology is selected only when it
is a part of min cost solution at the root
Example of Plate-based Adjustment
Methodology Flow
1. Timing-driven Steiner tree ( C-Tree )
2. Plate-based adjustment
3. Local blockage avoidance• If a wire overlaps with blockage, it is
rerouted within its local tiles
4. Van Ginneken style buffer insertion
Experiment Setup
• Integrated into industrial physical synthesis tool
• Three testcases – 155K, 334K and 293K cells– 209, 848 and 18 blockages
• FOM(Figure of Merit): cumulative negative slacks
Experimental Result on FOM
-30000
-25000
-20000
-15000
-10000
-5000
0
test1 test2 test3
baseline
porosity
Resource Consumption
• Wirelength increase is negligible
• CPU time is increased significantly– Plate-based adjustment– More candidate buffer locations enabled
Result Regardless Porosity
Result Considering Porosity
Conclusion
• Porosity need to be considered in buffered Steiner tree construction
• A plate-based adjustment in a four-stage flow is proposed as a solution
• Experiments with industrial physical synthesis system show encouraging results
Thank you !Thank you !