3D-Flow: Flow-based Standard Cell Legalization for 3D ICs

The standard-cell placement legalization is a critical step in the physical design. The emerging 3D ICs have brought challenges to traditional legalizers on efficiency and effectiveness. In this work, we present a fast flow-based legalization algorithm, 3D-Flow, that minimizes cell displacement in a 3D solution space. Our legalizer resolves overflowed bins by finding the shortest augmenting path on a 3D grid graph, utilizing an effective branch-and-bound algorithm. Moreover, a post-optimization with a cycle-canceling algorithm is proposed to minimize the maximum displacement. Our approach leverages the global perspective inherent in network flow methods, considering multiple dies in 3D ICs to minimize cell displacement. Experimental results on ICCAD 2022 and 2023 contest benchmarks demonstrate our proposed algorithm achieves up to 13% and 43% less average and maximum cell displacement compared to state-of-the-art legalizers in a similar runtime.