On the computational power of the light: An optical method for the subgraph isomorphism problem

Abstract

NP-complete and NP-hard problems, such as subgraph isomorphism, are well-known benchmarks to evaluate computation power of unconventional computing approaches. Optical computing, as one of the most important unconventional approaches, has determinant features such as massive parallelism that allows us to solve hard computational problems in an efficient time, while in the similar situations conventional computers require exponential time. In this paper, we solve subgraph isomorphism, as an NP-complete problem, using optical computing in a polynomial time after a polynomial preprocessing time. The proposed method has two main steps: first, possible solution space of the problem is generated using an optical manner and then all invalid solutions are eliminated from the space by several designed optical filters. The filters are made in the preprocessing phase in a polynomial time while the space of each filter is exponential. In this study, we have provided a solution to the YES/NO decision version of the problem.