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Mixed-cell-height circuits have become popular in advanced technologies for better power, area, routability, and performance tradeoffs. With technology and region constraints imposed by modern circuit designs, the mixed-cell-height legalization problem has become even more challenging. Additionally, an ideal legalization method should minimize both the average and maximum cell movements to preserve the quality of a given placement as much as possible. In this article, we present an effective and efficient mixed-cell-height legalization algorithm to consider technology and region constraints while minimizing the average and maximum cell movements. We first present a fence region handling technique to unify the fence regions and the default region. To obtain a desired cell assignment, we then propose a movement-aware cell reassignment method by iteratively reassigning cells in locally dense areas to their desired rows. After cell reassignment, a technology-aware legalization is presented to remove cell overlaps while satisfying the technology constraints. Finally, we propose a technology-aware refinement to further reduce the average and maximum cell movements without increasing the technology constraints violations. Compared with the champion of the 2017 CAD Contest at ICCAD and the state-of-the-art work, experimental results based on the 2017 CAD Contest at ICCAD benchmarks show that our algorithm achieves the best average and maximum cell movements and significantly fewer technology constraint violations, in a comparable runtime. The experimental results based on the modified 2015 ISPD Contest benchmarks also demonstrate the effectiveness of our algorithm in minimizing the average and maximum cell movements, compared with state-of-the-art mixed-cell-height legalizers. [ABSTRACT FROM AUTHOR]

In this paper, we consider the triple patterning lithography layout decomposition problem. To address the problem, a discrete relaxation theory is built. For designing a discrete relaxation based decomposition framework, we propose a surface projection method for identifying native conflicts in a layout, and then constructing the conflict graph. Guided by the theory, the conflict graph is reduced to small size subgraphs by vertex removals, which is a discrete relaxation. Furthermore, by ignoring stitch insertions and assigning weights to features, the layout decomposition problem on the small subgraphs is further relaxed to a 0-1 program, which is solved by the Branch-and-Bound method. To obtain a feasible solution of the original problem, legalization methods are introduced to legalize a relaxation solution. At the legalization stage, we prior utilize one-stitch insertion to eliminate conflicts, and use a backtrack coloring algorithm to obtain a better solution. We test our decomposition approach on the ISCAS-85 & 89 benchmarks. Comparisons of experimental results show that our approach finds solutions of some benchmarks better than those by the state-of-the-art decomposers. Especially, according to our discrete relaxation theory, some optimal decompositions are obtained. [ABSTRACT FROM PUBLISHER]