Fault-tolerant hamiltonian cycles and paths embedding into locally exchanged twisted cubes

Abstract

The foundation of information society is computer interconnection network, and the key of information exchange is communication algorithm. Finding interconnection networks with simple routing algorithm and high fault-tolerant performance is the premise of realizing various communication algorithms and protocols. Nowadays, people can build complex interconnection networks by using very large scale integration (VLSI) technology. Locally exchanged twisted cubes, denoted by (s + t + 1)-dimensional LeTQs,t, which combines the merits of the exchanged hypercube and the locally twisted cube. It has been proved that the LeTQs,t has many excellent properties for interconnection networks, such as fewer edges, lower overhead and smaller diameter. Embeddability is an important indicator to measure the performance of interconnection networks. We mainly study the fault tolerant Hamiltonian properties of a faulty locally exchanged twisted cube, LeTQs,t − (fv + fe), with faulty vertices fv and faulty edges fe. Firstly, we prove that an LeTQs,t can tolerate up to s − 1 faulty vertices and edges when embedding a Hamiltonian cycle, for s ⩾ 2, t ⩾ 3, and st. Furthermore, we also prove another result that there is a Hamiltonian path between any two distinct fault-free vertices in a faulty LeTQs,t with up to (s − 2) faulty vertices and edges. That is, we show that LeTQs,t is (s − 1)-Hamiltonian and (s − 2)-Hamiltonian-connected. The results are proved to be optimal in this paper with at most (s − 1)-fault-tolerant Hamiltonicity and (s − 2) fault-tolerant Hamiltonian connectivity of LeTQs,t.

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Acknowledgements

We would like to express our sincerest appreciation to Prof. Guoliang Chen for his constructive suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1905211, 61872196, 61902195 and 61972272), Natural Science Foundation of Jiangsu Province (BK20200753), Natural Science Fund for Colleges and Universities in Jiangsu Province (General Program, 19KJB520045), NUPTSF (NY219151, NY219131).

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Correspondence to Jianxi Fan.

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Weibei Fan received the BS and MS degrees from Henan University of Urban Construction and Henan University, China in 2011 and 2014, respectively, and received the PhD degree in Computer Science from Soochow University, China from 2019. He is currently an associate professor incomputerscience at Nanjing University of Posts and Telecommunications, China. His research interests include parallel and distributed systems, cloud computing, and interconnection networks.

Jianxi Fan received the BS, MS, and PhD degrees in Computer Science from the Shandong Normal University, Shandong University, and the City University of Hong Kong, China in 1988, 1991, and 2006, respectively. He is currently a professor in the School of Computer Science and Technology at the Soochow University, China. He was a visiting scholar in the Department of Computer Science at Montclair State University (May 2017–August 2017) and a senior research fellow in the Department of Computer Science at the City University of Hong Kong (May 2012–August 2012). His research interests include parallel and distributed systems, interconnection architectures, data center networks, algorithms, and graph theory.

Zhijie Han received the MS and PhD degrees computer science from Henan University and Soochow University, China in 2006 and 2009, respectively. He is currently a vice professor in the school of computer and information engineering, Henan University, China. His research interests include parallel and distributed computing, cloud computing, and big data.

Peng Li received the PhD degree from Nanjing University of Posts and Telecommunications (NUPT), China in 2013. Currently, he is an associate professor and Master Supervisor in NUPT. He has managed a number of research projects supported by the National Natural Science Foundation of China and research projects supported by the Ministry of Jiangsu Province. His main research interests include parallel and distributed computing, cloud computing computer communication networks (especially in Wireless Sensor Networks, Ad Hoc Network) and information security.

Yujie Zhang received the BS and MS degrees from Henan Polytechnic University and Henan University, China in 2012 and 2016, respectively. He is currently working toward the PhD degree in information security at Nanjing University of Posts and Telecommunications, China. His research interests include cloud computing, cooperative communications, and information security.

Ruchuan Wang researched on graphic processing at the University of Bremen and program design theory Ludwig Maximilian Muenchen Unitversitaet, German from 1984 to 1992. He is currently a professor and the PhD supervisor in the School of Computer, Nanjing University of Posts and Telecommunications, China. His major research interests include parallel and distributed systems, wireless sensor networks and information security.

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Fan, W., Fan, J., Han, Z. et al. Fault-tolerant hamiltonian cycles and paths embedding into locally exchanged twisted cubes. Front. Comput. Sci. 15, 153104 (2021). https://doi.org/10.1007/s11704-020-9387-3

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Keywords

  • interconnection network
  • fault-tolerant
  • LeTQ s,t
  • hamiltonian cycle
  • hamiltonian path