Two-way partitioning based on direction vector

In the spectral method, the vertices in a graph can be mapped into the vectors in d-dimensional space, thus the vectors are partitioned instead of vertices to obtain graph partitioning. In this paper, we show a method to obtain optimal two-way vector partitioning based on an optimal direction vector. As the problem to find the optimal direction vector is NP-problem, we propose an efficient heuristic to obtain high quality direction vector. As we approximate a given netlist into the graph and only use ten eigenvectors in practice, there is a chance to improve the solution quality by local optimization. Fiduccia-Mattheyses algorithm is employed as a post processing. Compared with FM and MELO, the proposed algorithm PDV reduces cutsize on the average 40% and 20.5%, respectively.