1. mPL 5 Overview ISPD 2005 Placement Contest Entry
Tony Chan2, Jason Cong1, Joe Shinnerl1, Kenton Sze2, Michalis Romesis1, Min Xie1
1VLSI CAD Lab, Computer Science Department
2Mathematics Department
University of California, Los Angeles

2. Multiscale Optimization Framework
Given problem
Coarsening (Clustering)
Problem size decreases
Interpolation &
Relaxation (optimization)
Explores different scales of the solution space at different levels
Supports VERY FAST and SCALABLE methods
Supports inclusion of complicated objectives and constraints
Successful across MANY DIVERSE applications
12/9/2018
UCLA VLSICAD LAB

3. Multiscale Placement Vocabulary
Coarsening: build a hierarchy of problem approximations by generalized recursive clustering (or partitioning)
Relaxation: improve the placement at each level by iterative optimization
Interpolation: transfer coarse-level solution to adjacent, finer level (generalized declustering)
Multilevel Flow: multiple traversals over multiple hierarchies (V-cycle variations)
12/9/2018
UCLA VLSICAD LAB

4. A Brief History of mPL UNIFORM CELL SIZE NON-UNIFORM CELL SIZE
Relative Wirelength
A Brief History of mPL
mPL 1.1
FC-Clustering
added partitioning to legalization
mPL 1.0 [ICCAD00]
Recursive ESC clustering
NLP at coarsest level
Goto discrete relaxation
Slot Assignment legalization
Domino detailed placement
UNIFORM
CELL SIZE
mPL 2.0
RDFL relaxation
primal-dual netlist pruning
mPL 3.0 [ICCAD 03]
QRS relaxation
AMG interpolation
multiple V-cycles
cell-area fragmentation
mPL 4.0
improved DP
better coarsening
backtracking V-cycle
NON-UNIFORM
CELL SIZE
mPL 5.0
Multilevel Force-Directed
2000
2001
2002
2003
2004
year
12/9/2018
UCLA VLSICAD LAB

5. Coarsening by Recursive Aggregation
First-Choice Clustering (hMetis [Karypis 1999]).
Merged Nets
Merge each vertex with its “best” neighbor
12/9/2018
UCLA VLSICAD LAB

6. Weighted Interpolation (Generalized Declustering)
Transfer a partial solution from a coarser level to its adjacent finer level
Place a component ( ) at the weighted average of the positions of the clusters containing its neighbors
Place representative components
Place others by weighted interpolation
12/9/2018
UCLA VLSICAD LAB

7. mPL5 Generalized Force-Directed Placement
Smooth the density constraints by solving a Helmholtz Equation:
Assume Neumann boundary conditions: forces pointing outside the chip boundary are zero:
Log-sum-exp smooth approximation to half-perimeter wirelength [Naylor 2001; Kahng and Wang 2004]:
12/9/2018
UCLA VLSICAD LAB

8. mPL5 Nonlinear-Programing Solution
Using the Uzawa algorithm to solve the above nonlinear constrained minimization problem, we iteratively solve
No matrix storage and no second derivatives are computed.
Separate updates for separate lagrange multipliers; the bin-density constraints are NOT lumped together
Use multilevel approach to speed-up computation and better quality
12/9/2018
UCLA VLSICAD LAB

9. Iterated Multilevel Flow
Make use of placement solution from 1st V-cycle
Geometric based
FC clustering
First Choice (FC)
clustering
12/9/2018
UCLA VLSICAD LAB

10. Legalization
The Patoma flow for guaranteed legalizability (ASPDAC 2005) is not needed for the ISPD05 contest benchmarks…
…because they have so much white space.
Work on Patoma-enabled mPL (“mPL6”) for large-scale, high-utilization cases ( even above 99%!) continues.
In the presence of many fixed macros, we sometimes reduce HPWL more than 30% (!) simply by assigning cells to obstacle-free subregions before placing them.
Can apply LP/network-flow techniques.
Preserve the global placement as much as possible (tetris-like)
12/9/2018
UCLA VLSICAD LAB

11. Important command-line options for ISPD 2005 suite
-shrinkRegion, -shrinkRatio
Usually get shorter wirelength by packing cells
Can pack cells to left, right, or center to a user-specified level of utilization
-addDummyCells
The best configuration may be highly nonuniform
Adding unconnected “dummy” filler cells enables mPL to find good nonuniform placements
-legalRegion
Divide the chip into rectangular regions defined by fixed-block boundaries.
Assign cells to subregions first, then legalize separately within the subregions.
-GFD::Gamma
Can fine tune the rate at which the weight of spreading forces is increased relative to wirelength forces
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UCLA VLSICAD LAB

12. Improvements by parameter tuning
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UCLA VLSICAD LAB

13. Acknowledgments Collaborators Sponsors Chin-Chih Chang, Cadence
Tim Kong, Magma
Yuchun (Clara) Ma, UCLA CS
Xin Yuan, IBM
Sponsors
SRC Contracts 99-TJ-686 and 2003-TJ-1091
NSF Awards CCF & CCR
ONR Contract N
12/9/2018
UCLA VLSICAD LAB