Rectilinear Steiner Tree (RST) construction is a fundamental problem in very large scale integration (VLSI) physical design. Its applications include placement and routing in VLSI physical design automation (PDA) where wire length and timing estimations for signal nets are obtained. In this paper, a pseudo-Boolean satisfiability (PB-SAT)-based approach is presented to solve rectilinear Steiner tree problem. But large nets are a bottleneck for any SAT-based approach. Hence, to deal with large nets, a region-partitioning-based algorithm is taken into consideration, which eventually achieves a reasonable running time. Furthermore, a clustering-based approach is also explored to improve the partitioning of nets by identifying clusters and then applying a heuristic-based approach to get the minimum wire length for each set of the clusters. Experimental results obtained by these techniques show that the proposed algorithm can solve the RST problem very effectively even on large circuits and it outperforms the widely used RST algorithm FLUTE with 3[Formula: see text][Formula: see text][Formula: see text]to 9[Formula: see text][Formula: see text][Formula: see text]speedups.
Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem
