COALA: Concurrently Assigning Wire Segments to Layers for 2D Global Routing

Two-dimensional (2D) global routing followed by layer assignment is a common and popular strategy to obtain a good trade-off between runtime and routing performance. Yet, the huge gap between 2D routing patterns and the final 3D routing paths often results in inevitable overflow after layer assignment. State-of-the-art 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 paper 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 re-routing procedure that greatly reduces inevitable overflows. Experimental results show that compared to the sequential layer assignment solutions that also refined by the same re-routing procedure, the proposed framework can averagely reduce the maximum overflow in a tile by 32% and reduce the number of tiles with overflows by 28% with much less runtime, which shows the significant advantage of concurrent layer assignment over sequential methods.