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Constrained ‘Modern’ Floorplanning

The Constrained Modern Floorplanning Problem (CMFP) poses challenges in efficiently designing layout with fixed die formulation. This paper explores a novel approach combining Min Cost Max Flow based floorplanning and a postprocessing step to enhance feasibility. Using a proposed design flow, the study showcases the benefits of a bound-feasible solution while addressing connectivity concerns. Experiment results and comparison of cost schemes demonstrate the effectiveness of the methodology. Future work aims to refine the postprocessing step for practical applicability and tackle infeasible inputs effectively.

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Constrained ‘Modern’ Floorplanning

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  1. Constrained ‘Modern’ Floorplanning Yan Feng Dinesh P. Mehta Colorado School of Mines Hannah Yang Intel

  2. Motivation/Assumption • Fixed die formulation with zero whitespace . (A. B. Kahng, ISPD 2000) • Modules shapes need not be restricted to rectangles, L-shapes, etc. (A. B. Kahng, ISPD 2000) • Approximate locations and sizes for modules are already known from quadratic placement, force-directed placement, or human design.

  3. Input Make suggestions to make input feasible Min Cost Max Flow Based Floorplanner Postprocessing Step Proposed Design Flow No Bound-Feasible Yes No Connected? Yes

  4. (0,0) (0,0) A B A B C C (100,100) (100,100) The Constrained Modern Floorplanning Problem(CMFP) • The CMFP problem is NP-hard.

  5. Feasibility Analysis Area(BC) = 8000 A B Required(BC) = 8500 C

  6. C B A E D Feasibility Analysis (0,0) (300,200)

  7. 4 5 2 1 11 12 10 6 7 9 15 14 Region Identification 3 C A B E 13 D

  8. Flow-based Feasibility Analysis If the maximum network flow of graph is equal to the total required area of modules then the input is feasible.

  9. Experiment result (ami 33)

  10. Floorplanning • The result of Max Flow algorithm does not guarantee connectivity. • Min Cost Max Flow Problem: each edge also has a cost a(u,v). So if f(u,v) units flow over edge (u,v), we incur a cost of a(u,v)f(u,v). • Computes a maximum flow as before, but finds one of min cost. • Post Processing Step • greedy algorithm B A A AB B

  11. Cost Assignment Schemes • The cost is assigned based on BFS on each region of module. • Compromise BFS: involves adding vertices & edges to the flow graph. Details in paper. • Improved BFS: combination of BFS & CBFS. 1 2 1 0 1 2 1 2

  12. Comparison of Cost Schemes • The initial input (center position) is obtained from previous SA result (ami33 & ami49). • Size of constraining rectangle ranges from 1.96 to 3.24 times of modules’ required area. • Using C++ & LEDA and the running time is about 5 secs.

  13. Sample output: ami49

  14. Future Work • A more systematic post processing step to obtain a practical result. • How to convert a infeasible input into a feasible one.

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