FPGA Placement by Graph Isomorphism

FPGA placement and routing are still challenging problems. Given the increased diversity of logic and routing resources on FPGA chips, it seems appropriate to tackle the placement problem as a mapping between the nodes and edges in a circuit graph to compatible resources in the architecture graph. We explore utilizing graph isomorphism algorithms to perform FPGA placement. We use a hierarchical approach in which the circuit and architecture graphs are simultaneously clustered to reduce the size of the search space, and then a novel reductive graph product method is used to solve the isomorphism problem. The graph product algorithm is called reductive as it eliminates a linear number of candidates at every step of the search process, reducing the number of candidate nodes by approximately 1/3. Compared to the annealing-based placement tool VPR 5.0, we achieve approximately 40% improvement in placement runtime, while improving the critical path delay by about 7% and wire length by 5%, while demanding 1.3% more channels on average.