元件擺放在現今的實體設計流程之中是非常關鍵的步驟，其中元件擺放
的可繞度早已被廣泛討論。在本篇論文中，針對具有巨集元件的混合電路，
我們探索了使用擺放指引來緩解繞線壅塞並減少設計規則違反的可能性。
藉由提取電路中元件的連接資訊以及標準元件對於巨集元件的相對關係，
我們使用圖神經網路對每個標準元件生成一個嵌入，用來代表該元件在電
路之中的連接關係。接著，我們應用兩種知名的分群演算法上在該嵌入上
來產生擺放指引。因此，商業擺放器在擺放時會努力避免具有複雜連接性
之標準元件的碎片化。實驗結果顯示，相對於商業軟體針對壅塞問題的擺
放流程，我們的方法減少了 28% 的繞線溢出及 74% 的設計規則違反。由於
在擺放階段合適的考量可繞度，我們平均減少了 31% 的繞線執行時間。

Placement is a critical step in a modern physical design flow, and the routability of the placement result has been long discussed. In this thesis, we explore the
possibility of using soft placement guidance to mitigate routing congestion and reduce design rule violations for mixed-size designs. By extracting the connectivity
of cell instances and the relation between standard cells and each macro in a design using the graph neural network (GNN), we generate an embedding for each
standard cell representing connectivity information in the circuit. Then, we apply
two renowned clustering algorithms to the embeddings and create the soft placement guidance. By adding the soft placement guidance to a commercial placer,
the placer will strive to avoid the fragmentation of standard cells with dense connections in the placement stage. Experimental results show that our methodology
helps the commercial tool reduce 28% routing overflow and avoid 74% design rule
violations. Because of properly considering routability in the placement stage, it
also helps reduce 31% routing runtime on average.

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . 4
1.3 Our Contributions . . . . . . . . . . . . . . . . . . . . . 5
1.4 Thesis Organization . . . . . . . . . .. . . . . . . . . . . 5
2 Related Works . .. . . . . . . . . . . . . . . . . . . . . . 6
2.1 Routability-driven Placement . . . . . . . . . . . . . . . . 6
2.2 Applications of Placement Guidance . . . . . . . . . . . . . 7
3 Methodology . . . . . . . . . . . .. . . . . . . . . . . . . . 9
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Node Embeddings Generation . . . . . . . . . . . . . . . . . 10
3.2.1 Graph Creation . . . . . . . . . . . . . . . . . . . . . . 10
3.2.2 Node Bundling . . . . . . . . . . . . . . . . . . . . . . 11
3.2.3 Initial Node Features Creation . . . . . . . . . . . . . . 11
3.2.4 GNN Node Embeddings Learning . . . . . . . . . . . . . . . 13
3.3 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 Experimental Results . . . . . . . . . . . . . . . . . . . . . 19
4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . 19
4.2 Results . . . . . . . .. . . . . . . . . . . . . . . . . . . 19
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ii
References . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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