Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Model-based dummy feature placement for oxide chemical-mechanical polishing manufacturability
Proceedings of the 37th Annual Design Automation Conference
Practical iterated fill synthesis for CMP uniformity
Proceedings of the 37th Annual Design Automation Conference
Monte-Carlo algorithms for layout density control
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A fast approximation scheme for fractional covering problems with variable upper bounds
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
ISQED '05 Proceedings of the 6th International Symposium on Quality of Electronic Design
Filling algorithms and analyses for layout density control
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Area fill synthesis for uniform layout density
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
CMP Fill Synthesis: A Survey of Recent Studies
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast Dummy-Fill Density Analysis With Coupling Constraints
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Randomized Greedy Method for Rectangular-Pattern Fill Problems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An efficient method for gradient-aware dummy fill synthesis
Integration, the VLSI Journal
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To reduce chip-scale topography variation in Chemical Mechanical Polishing (CMP) process, dummy fill is widely used to improve the layout density uniformity. Previous researches formulated the dummy fill problem as a standard Linear Program (LP). However, solving the huge linear program formed by real-life designs is very expensive and has become the hurdle in deploying the technology. Even though there exist efficient heuristics, their performance cannot be guaranteed. In this paper, we develop a dummy fill algorithm that is both efficient and with provably good performance. It is based on a fully polynomial time approximation scheme by Fleischer [4] for covering LP problems. Furthermore, based on the approximation algorithm, we also propose a new greedy iterative algorithm to achieve high quality solutions more efficiently than previous Monte-Carlo based heuristic methods. Experimental results demonstrate the effectiveness and efficiency of our algorithms.