Closing the Smoothness and Uniformity Gap in Area Fill Synthesis

1. Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Closing the Smoothness and Uniformity Gap in Area Fill Synthesis Y. Chen,A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU) http://vlsicad.ucsd.edu

2. Gap! floating window with maximum density fixed dissection window with maximum density The Smoothness Gap • Large gap between fixed-dissection and floating window density analysis • Fill result will not satisfy the given bounds • Despite this gap observation in1998, all existing filling methods fail to consider the potential smoothness gap

3. Accurate Layout Density Analysis • Optimal extremal-density analysis with complexity intractable • Multi-level density analysis algorithm • shrunk on-grid windows are contained by arbitrary windows • any arbitrary window is contained by a bloated on-grid window • gap between bloated window and on-grid window accuracy fixed dissection window arbitrary window W shrunk fixed dissection window bloated fixed dissection window tile

4. Type II: max density variation of every cluster of windows which cover one tile • Type III: max density variation of every cluster of windows which cover tiles Local Density Variation • Type I: max density variation of every r neighboring windows in each row of the fixed-dissection

5. Computational Experience • The window density variation and violation of the maximum window density in fixed-dissection filling are underestimated • The solutions with the best Min-Var objective value do not always have the best value in terms of local smoothness • LP with combined objective achieves the best comprehensive solutions

6. Thank you!