隨著先進製程演進，複雜的圖案會影響電路的可製造性以及生產良率。
因此，我們需要多元件間距限制來提高電路的可製造性和生產良率。
然而，目前的做法只能處理兩元件間距限制，這不僅會錯失擺放的可行解也會增加元件的移動距離。
在這篇論文中，我們提出了一個針對多元件間距限制的兩階段細部擺置方法。
在第一個階段，我們提出可允許元件翻轉、元件位移和相鄰元件交換的單列動態規劃為基礎的方法(IRM)來解決大部分違反多元件間距限制之情況，並且同時減少元件的移動距離和線長的增加。
值得注意的是在第一個階段我們著重於局部調整元件的擺放位置, 因此將有助於保持初始的線長、時序等。
在第二階段中，我們提出一個整數線性規劃為基礎的方法(GM)來解決剩餘違反多元件間距限制之情況。
實驗數據顯示了我們的方法可以有效率地消除所有違反多元件間距限制的情形。

In advanced manufacturing processes, the specific complex patterns affect manufacturability and yield; therefore,
multi-cell spacing constraints have been required to improve yield and for design for manufacturability.
However, the current practice can only handle 2-cell spacing constraints, which overkill the placement solutions and increase cell displacement. In this paper, we develop a two-phase method to handle multi-cell spacing constraints during detailed placement. In the first phase, we propose a single-row dynamic programming (SRDP)-based Intra-Row Move (IRM) method which allows cell flipping, cell shifting, and adjacent cell swapping, the objective is to resolve most of the constraint violations while minimizing total cell displacement and wirelength increment. Note that the first phase induces highly localized changes which will help preserve the initial wirelength, timing, etc. In the second phase, we propose an ILP-based Global Move (GM) method to resolve any remaining constraint violations. Experimental results show that our method can effectively handle multi-cell spacing constraints.

誌謝 i
Acknowledgements ii
摘要 iii
Abstract iv
1 Introduction 1
1.1 Detailed Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Previous Works and Our Contributions . . . . . . . . . . . . . . . . . . 3
1.4 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Preliminaries 6
2.1 Multi-Cell Spacing Constraints . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Algorithm 9
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Constraint and Layout Analysis . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Intra-Row Move (IRM) . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.1 Cost Computation . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3.2 Dynamic Programming Formulation . . . . . . . . . . . . . . . 12
3.4 Global Move (GM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Experimental Results 20
5 Conclusion 26
References 27

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