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History-based VLSI Legalization using Network Flow

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

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History-based VLSI Legalization using Network Flow

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  1. History-based VLSI Legalization using Network Flow Minsik Cho, HaoxingRen, Hua Xiang, RuchirPuri DAC’10

  2. Outline • Introduction & Contribution • Problem Formulation • Algorithm • Network Flow Formulation • Flow Realization • Region Placement • History Learning • Experimental Results • Conclusion & Future Work

  3. 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.

  4. 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

  5. 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

  6. Problem Formulations (cont) Maximum deviation Average weighted sum

  7. 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.

  8. Algorithm Flow

  9. Example: Compare Flow and Greedy

  10. Step 1: Network Flow Might move partially Times of history failed

  11. 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 λcan reduce run time. • It returns Failure if the problemis unsolvable.

  12. 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].

  13. Step 4: History Learning • To avoid unrealizable flow, increasing the history factor h[wi][r][p] for the cost expensive enough. Success flow onthe 5th iteration

  14. 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 caninsert the edges by user defined. (reduce |E|) • Using hierarchical approach to reduce |R|.

  15. 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

  16. Experiment Results (cont) • Failure rate comparison

  17. Experiment Result (cont) • Compare QoR with NTUPlace

  18. 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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