Approximate Maximum Common Sub-graph Isomorphism Based on Discrete-Time Quantum Walk

Maximum common sub-graph isomorphism (MCS) is a famous NP-hard problem in graph processing. The problem has found application in many areas where the similarity of graphs is important, for example in scene matching, video indexing, chemical similarity and shape analysis. In this paper, a novel algorithm Qwalk is proposed for approximate MCS, utilizing the discrete-time quantum walk. Based on the new observation that isomorphic neighborhood group matches can be detected quickly and conveniently by the destructive interference of a quantum walk, the new algorithm locates an approximate solution via merging neighborhood groups. Experiments show that Qwalk has better accuracy, universality and robustness compared with the state-of-the-art approximate MCS methods. Meanwhile, Qwalk is a general algorithm to solve the MCS problem approximately while having modest time complexity.