Two-dimensional (2-D) global routing followed by layer assignment is a common and popular strategy to obtain a good tradeoff between runtime and routing performance. Yet, the huge gap between 2-D routing patterns and the final 3-D routing paths often results in inevitable overflow after layer assignment. State-of-the-art (SOTA) studies on layer assignment usually adopt dynamic programming-based approaches to sequentially find an optimal solution for each net in terms of overflow or/and the number of vias. However, a fixed assignment ordering severely restricts the solution space, and the distributed overflows can hardly be resolved with any existing refinement approach. This article proposes a novel layer assignment framework that concurrently considers all the wire segments of nets and iteratively assigns them from the lowest available layer to the highest one. The concurrent scheme facilitates the maximal utilization of routing resource on each layer, contributing to an effective rerouting procedure that greatly reduces inevitable overflows. Based on the proposed framework, we further propose an obstacle-aware strategy that can mitigate obstacle-induced inevitable overflows in the original framework. Experimental results show that compared to an implemented sequential layer assignment approach based on SOTA techniques and refined by the well-known overflow/congestion reduction rip up and rerouting procedure, the proposed concurrent layer assignment framework (COALA) brings great improvements in the overflow reduction and runtime efficiency, which shows the significant advantage of the concurrent layer assignment scheme over sequential methods. The improvement is also verified in detailed routing, where the proposed COALA framework contributes to sparser routing results with fewer vias and design rule violations (DRVs).

中文翻译：

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COALA：同时将线段分配给图层以进行二维全局布线

二维 (2-D) 全局路由后接层分配是一种常见且流行的策略，可以在运行时和路由性能之间取得良好的折衷。然而，2-D 布线模式与最终 3-D 布线路径之间的巨大差距常常导致层分配后不可避免的溢出。关于层分配的最新 (SOTA) 研究通常采用基于动态规划的方法，根据溢出或/和过孔数量依次为每个网络找到最佳解决方案。然而，固定的分配顺序严重限制了解决方案空间，分布式溢出很难用任何现有的改进方法来解决。本文提出了一种新颖的层分配框架，该框架同时考虑网络的所有线段，并将它们从最低可用层迭代分配到最高层。并发方案有助于最大限度地利用每一层上的路由资源，有助于有效的重新路由过程，从而大大减少不可避免的溢出。基于所提出的框架，我们进一步提出了一种障碍感知策略，可以减轻原始框架中障碍引起的不可避免的溢出。实验结果表明，与基于 SOTA 技术并通过众所周知的溢出/拥塞减少撕裂和重新路由程序改进的顺序层分配方法相比，所提出的并发层分配框架（COALA）在减少溢出和运行时效率方面带来了很大的改进，这显示了并发层分配方案相对于顺序方法的显着优势。这种改进也在详细布线中得到验证，其中提议的 COALA 框架有助于通过更少的过孔和设计规则违规 (DRV) 获得更稀疏的布线结果。