History-based VLSI Legalization using Network Flow

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```					History-based VLSI Legalization
using Network Flow
Minsik Cho, Haoxing Ren, Hua Xiang, Ruchir Puri
DAC’10
Outline
   Introduction & Contribution
   Problem Formulation
   Algorithm
   Network Flow Formulation
   Flow Realization
   Region Placement
   History Learning
   Experimental Results
   Conclusion & Future Work
Introduction
   The high density of design in a chip affects the entire physical
design.
   Take care of placement can reduce the complexity of the
following stages:
   buffering, gate sizing, routing, etc.
   The main goal of placement
   Locate all the objects without overlap
   Satisfying each kinds of design objectives.
   Legalization is an important step between global and detail
placement to remove all the overlaps with minimum
perturbation or impaction.
Contribution
   A novel gate-centric MCMF formulation
   Optimize the deviation for each gate better
   History scheme can be integrated smoothly

   Incorporate a history-based technique into a new
network flow formulation

   Propose efficient techniques to realize a flow into gate
movements based on a Subset-sum problem
Problem Formulations
   A rectangle chip is partitioned into equal-sized circuit
rows, and each row is further divided into block-free
regions.
   The Manhattan distance between these two positions is
defined as deviation
Problem Formulations (cont)

Maximum deviation
Average weighted sum
Further Issues
   Base on network flow, how to set the sources and sinks
by this formula?
   Set all the gates in one of overflow regions as sources, other
regions as sinks.
   How to solve that general network flow cannot model
discrete sizes of gates?
   Using unbounded or maximum width size of gate as limit of
flow and do the Flow Realization.
   How to calculate the deviation of the y-value?
   Using the center Yr+Wr/2 to evaluate the deviation, and do
the Region Placement.
Algorithm Flow
Example: Compare Flow and Greedy
Step 1: Network Flow
Might move partially

Times of history failed
Step 2: Flow Realization
   There is a partial flow from A to the empty space
   Solve Subset-sum problem(NP class)
   Partition into two set and fit the
regions with cheapest solution.
   We set the size solution T < λ
   Control the bounded flow and λ
can reduce run time.
   It returns Failure if the problem
is unsolvable.
Step 3: Region Placement
   Find y-value of all gates in a region for minimum deviation
is NP-Hard.
   Order the gates according to the center location (xi, yi+wi/2)
rather than (xi, yi), and it provides the less deviation according
to experience.
   In case of overflow region, we temporarily scale down wi with
Wr/Or, just make placement fesiable.
   Solve this problem by single row placement refer to [3,4,7, 11].
Step 4: History Learning
   To avoid unrealizable flow, increasing the history factor
h[wi][r][p] for the cost expensive enough.

Success flow on
the 5th iteration
Post-Optimization & Speedup
   When we get a legal solution, it is possible that some gates
have large deviation.
   Greedily move gates toward their initial position.
   Using Flow Realization with zero flow

   The complexity of network flow is:

   Boundle tightly coupled gates if the total width less than maximum
width in library, it can reduce |I| effectively.
   In most case, a gate migrates to the nearby regions, we can
insert the edges by user defined. (reduce |E|)
   Using hierarchical approach to reduce |R|.
Experiment Results
   Environment
   Implement in C++
   2.4GHz Linux machine with 4G RAM
   Competitor
   NTUPlace3-LE, FastPlace3, Dragon2006, BonnL
   Benchmark
   45nm with mixed-sized blockages and fixed gates
   From the industrial global placer
   Ignore
   Wire length optimization
Experiment Results (cont)
   Failure rate comparison
Experiment Result (cont)
   Compare QoR with NTUPlace
Conclusion & Future Work
   Using History-based MCMF to solve the general
problems cannot solve by normal MCMF.
   Simultaneously legalization often get better QoR.

   Using the history-based technique
   The assignment problem with the in-flow of a souce more than
one.
   The cost of SA-based problem.
   By solving the Subset-sum problem
   We can solve network flow out of bound to get more
optimization chances.

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