Multi-Way Partitioning Via Spacefilling Curves and Dynamic Programming

Spectral geometric embeddings of a circuit netlist can lead to fast, high quality multi-way partitioning solutions. Furthermore, it has been shown that d-dimensional spectral embeddings (d > 1) are a more powerful tool than single-eigenvector embeddings (d = 1) for multi-way partitioning [2] [4]. However, previous methods cannot fully utilize information from the spectral embedding while optimizing netlist-dependent objectives. This work introduces a new multi-way circuit partitioning algorithm called DP-RP. We begin with a d-dimensional spectral embedding from which a 1-dimensional ordering of the modules is obtained using a spacefilling curve. The 1-dimensional ordering retains useful information from the multi-dimensional embedding while allowing application of efficientalgorithms. We show that for a new Restricted Partitioning formulation, dynamic programming efficiently finds optimal solutions in terms of Scaled Cost [4] and can transparently handle user-specified cluster size constraints. For 2-way ratio cut partitioning, DP-RP yields an average of 45% improvement over KP [4] and EIG1 [6] and 48% improvement over KC [2].