在設計印刷電路板時，繞線過程中的全域繞線扮演關鍵角色，而繞線資源估計的準確性則會大幅影響全域繞線結果的好壞。在本篇論文中，我們提出了一個在有限的繞線資源情形下，針對印刷電路板中非關鍵訊號線的全域繞線器。此外，我們還研究了在初始繞線階段和優化階段中，用來決定繞線順序之繞線成本的設計概念。實驗結果顯示，與手工繞線相比，我們的全域繞線器在繞非關鍵訊號線時，可縮短完成時間且同時維持平均八成五的繞線完成率。

Global routing plays an important role in the routing process when designing
printed circuit boards (PCBs). The accuracy of routing resources estimation
greatly affects the quality of global routing results. In this thesis, we propose
a global router focusing on non-critical nets in PCBs when the limited routing
resources are present. Furthermore, we discuss the design concept of routing cost
which determines the routing order in the initial routing stage and refinement stage
of our router. Our experiments demonstrate that when compared with manual
routing, our global router achieves improvement in completion time while keeping
at least 85% routing completion rates.

1 Introduction 1
1.1 PCB and PCB Routing . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Our Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Overall Flow of Our Router and Routing Graph Construction
Stage 8
2.1 Overall Flow of Our Global Router . . . . . . . . . . . . . . . . . . 8
2.2 Routing Graph Construction Stage . . . . . . . . . . . . . . . . . . 9
2.2.1 Global Cells Construction . . . . . . . . . . . . . . . . . . . 9
2.2.2 Local Pin Pairs Identification . . . . . . . . . . . . . . . . . 9
2.2.3 Attribute Setting of Routing Graph . . . . . . . . . . . . . . 10
3 Initial Routing and Refinement Stages 13
3.1 Initial Routing Stage . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Refinement Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Rip-up and Reroute Ordering Determination . . . . . . . . . 15
3.2.2 Pin Pair Cost Update . . . . . . . . . . . . . . . . . . . . . 16
ii
4 Experimental Results 18
5 Conclusion 27
References 28

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