Many applications can be modeled as subgraph isomorphism problems. However, this problem is generally NP-complete and difficult to compute. A custom computing circuit is a prospective solution for such problems. This paper examines various accelerator designs, and compares them quantitatively from two points of view: cost and performance. An algorithm that is suited for hardware implementation is also proposed. The hardware for the proposed algorithm is much smaller on logic scale, and operates at a higher frequency than Ullmann's design. The prototype accelerator operates at 16.5 MHz on a Lucent ORCA 2C15A, which outperforms the software implementation of Ullmann's algorithm on a 400 MHz Pentium II.