24,131 research outputs found
FFTPL: An Analytic Placement Algorithm Using Fast Fourier Transform for Density Equalization
We propose a flat nonlinear placement algorithm FFTPL using fast Fourier
transform for density equalization. The placement instance is modeled as an
electrostatic system with the analogy of density cost to the potential energy.
A well-defined Poisson's equation is proposed for gradient and cost
computation. Our placer outperforms state-of-the-art placers with better
solution quality and efficiency
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
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Nanometer VLSI placement and optimization for multi-objective design closure
In a VLSI physical synthesis flow, placement directly defines the interconnection,
which affects many other design objectives, such as timing, power consumption,
congestion, and thermal issues. With the scaling of technology, the relative interconnect
delay increases dramatically. As a result, placement has become a bottleneck
in deep sub-micron physical synthesis. In this dissertation, I propose several
optimization algorithms from global placement, placement migration, timing driven
placements, to incremental power optimizations for multi-objective VLSI design
closure. The first work is DPlace, a new global placement algorithm that scales
well to the modern large-scale circuit placement problems. DPlace simulates the
natural diffusion process to spread cells smoothly over the placement region, and
uses both analytical and discrete techniques to improve the wire length. However,
global placement is never sufficient for multi-objective design closure, a variety of
design objectives have to be improved incrementally, such as timing, routing congestion,
signal integrity, and heat distribution. Placement migration is a critical step
to address the cell overlaps appearing during incremental optimizations. To achieve
high placement stability, I propose a computational geometry based placement migration
flow to cope with placement changes, and a new stability metric to measure
the “similarity” between two placements accurately. Our placement migration algorithm
has clear advantage over conventional legalization algorithms such that the
neighborhood characteristics of the original placement are preserved. For timing
closure in high performance designs, I present a linear programming based incremental
timing driven placement to improve the timing on critical paths directly.
I further present an efficient timing driven placement algorithm (Pyramids). Two
formulations of Pyramids are proposed, which are suitable for different optimization
stages in a physical synthesis flow. Both approaches find the optimal location
for timing of a cell in constant time, through computational geometry based approaches.
For fast convergence of design closure, placement should be integrated
with other optimization techniques. I propose to combine placement, gate sizing
and Vt swapping techniques to reduce the total power consumption, especially the
leakage power, which is becoming increasingly critical for nanometer VLSI design
closure.Electrical and Computer Engineerin
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