A Pseudo-Boolean Encoding Method for Rectilinear Steiner Arborescence in VLSI Routing

Zixuan Wang, Yunuo Cen, Xuanyao Fong

Abstract: This paper presents a novel Pseudo-Boolean Optimization (PBO) framework to solve the Rectilinear Steiner Minimum Arborescence (RSMA) problem, with a focus on the All-Quadrant RSMA scenario. Our framework is designed to compute exact solutions efficiently, even in the presence of isothetic rectilinear obstacles. We also introduce a reduction technique that can reduce more than 17% of the encoded variables and constraints to improve solving efficiency. Our method guarantees optimality and offers flexibility and adaptability for large-scale instances. The experimental results indicate that the proposed framework solves 82.3% of 40-point instances and 64.3% of 50-point instances within 300 seconds.