The Design and Evaluation of Data-Dependent Hardware for Subgraph Isomorphism Problem

Subgraph isomorphism problems have various important applications, while generally being NP-complete. Though Ullmann and Konishi proposed the custom circuit designs to accelerate subgraph isomorphism problem, they require many hardware resources for large problems. This study describes the design of data-dependent circuits for subgraph isomorphism problem with evaluation results on an actual FPGA platform. Data-dependent circuits are logic circuits specialized in specific input data. Such circuits are smaller and faster than the original circuit, although it is not reusable and involves circuit generation for each input. In the present study, the circuits were implemented on Xilinx XC2V3000 FPGA, and they successfully operated at a clock frequency 25MHz. In the case of graphs with 16 vertices, the average execution time is about 7.0% of the software executed on an up-to-date microprocessor (Athlon XP 2600+ of 2.1GHz clock). Even if the circuit generation time is included, data-dependent circuits are about 14.4 times faster than the software (for random graphs with 16 vertices). This performance advantage becomes larger for larger graphs. Two algorithms (Ullmann’s and Konishi’s) were examined, and the datadependent approach was found to be equally effective for both algorithms. We also examined two types of input graph sets, and found that the datadependent approach shows advantage in both cases. key words: FPGA, custom circuit, graph algorithm, NP-complete, partial evaluation