Introduction to algorithms
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
A VLSI artwork legalization technique based on a new criterion of minimum layout perturbation
Proceedings of the 1997 international symposium on Physical design
Symbolic layout compaction review
DAC '88 Proceedings of the 25th ACM/IEEE Design Automation Conference
Technology migration technique for designs with strong RET-driven layout restrictions
Proceedings of the 2005 international symposium on Physical design
Backend CAD flows for "restrictive design rules"
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Technology migration techniques for simplified layouts with restrictive design rules
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
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Traditionally, automatic design rule correction (DRC) problem is modeled as a Linear Program (LP) with design rules as difference constraints under minimum perturbation objective. This yields Totally Uni-Modular (TUM) constraint matrices thereby guaranteeing integral grid-compliant solutions with LP solvers. However, advanced technology nodes introduce per-layer grids or discrete tracks that result into non-TUM constraint matrices for the DRC problem. Consequently, LP solvers do not guarantee integral solutions. In this work, we propose a novel formulation using an 'un-rolling' technique. Our formulation guarantees TUM constraint matrices and hence integral multiple grid/track compliant solutions. We demonstrate its efficacy on layouts at advanced nodes.