繞線是IC設計流程中非常重要的過程。隨著超大型積體電路設計中的特徵尺寸不斷縮小，在繞線階段需要考慮越來越複雜的設計規則。通常，由於問題的複雜性，繞線問題可分為兩個階段：全域繞線和細部繞線。現今繞線流程在細部繞線階段初期中使用軌道分配方法減少問題複雜度。
受ISPD 2018競賽初始細部繞線的啟發，我們提出了一種基於軌道指派的初始細部繞線方法，該方法通過使用Steiner樹演算法完全連接每條繞線連線。我們通過商業工具評估我們的繞線結果，以證明我們的繞線方法的有效性。

Routing is a very important procedure in the IC design flow. As feature size in VLSI design continues to shrink, more and more complex design rules need to be considered during the routing phase. Typically, the routing problem can be divided into two stages due to the problem complexity: global routing, and detailed routing. A modern routing flow inserts one more method, track assignment, in the beginning of the detailed routing stage.
Inspired by the ISPD 2018 Contest Initial Detailed Routing, we propose an initial detailed routing approach based on track assignment, which also fully connects each net by using a Steiner tree algorithm. We evaluate our routing by a commercial tool to demonstrate the effectiveness of our routing approach.

Contents
1 Introduction 1
2 Preliminaries and Problem Formulation 4
2.1 DRC Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Short . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 Min Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.4 Parallel-Run Spacing . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.5 End-of-Line Spacing . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.6 Cut Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Routing Preference Metrics . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Routing Guide Honoring . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Wrong-Way Routing . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 O-Track Routing . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Our Initial Detailed Routing Approach 9
3.1 Track-Assignment-Based Congestion Analysis . . . . . . . . . . . . . 10
3.1.1 Segment Extraction . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.2 Initial Track-Assignment . . . . . . . . . . . . . . . . . . . . . 11
3.1.3 Reduction of Segment Overlaps . . . . . . . . . . . . . . . . . 11
3.2 Routing Pattern Connection . . . . . . . . . . . . . . . . . . . . . . . 12
4 Experimental Results 18
5 Conclusion 22

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