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MapEff: An Effective Graph Isomorphism Agorithm Based on the Discrete-Time Quantum Walk

by Kai Liu 1,2,*, Yi Zhang 1,2, Kai Lu 1,2, Xiaoping Wang 3,*, Xin Wang 1,2 and Guojing Tian 4
1
College of Computer, National University of Defense Technology, Changsha 410073, China
2
Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Changsha 410073, China
3
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
4
Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(6), 569; https://doi.org/10.3390/e21060569
Received: 18 March 2019 / Revised: 28 May 2019 / Accepted: 29 May 2019 / Published: 5 June 2019
Graph isomorphism is to determine whether two graphs have the same topological structure. It plays a significant role in areas of image matching, biochemistry, and information retrieval. Quantum walk, as a novel quantum computation model, has been employed to isomorphic mapping detection to optimize the time complexity compared with a classical computation model. However, these quantum-inspired algorithms do not perform well—and even cease to work—for graphs with inherent symmetry, such as regular graphs. By analyzing the impacts of graphs symmetry on isomorphism detection, we proposed an effective graph isomorphism algorithm (MapEff) based on the discrete-time quantum walk (DTQW) to improve the accuracy of isomorphic mapping detection, especially for regular graphs. With the help of auxiliary edges, this algorithm can distinguish the symmetric nodes efficiently and, thus, deduct the qualified isomorphic mapping by rounds of selections. The experiments tested on 1585 pairs of graphs demonstrated that our algorithm has a better performance compared with other state-of-the-art algorithms. View Full-Text
Keywords: graph isomorphism; isomorphic mapping; discrete-time quantum walk; graph mining; data mining graph isomorphism; isomorphic mapping; discrete-time quantum walk; graph mining; data mining
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Liu, K.; Zhang, Y.; Lu, K.; Wang, X.; Wang, X.; Tian, G. MapEff: An Effective Graph Isomorphism Agorithm Based on the Discrete-Time Quantum Walk. Entropy 2019, 21, 569.

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