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Node-to-set disjoint paths problem in cross-cubes

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Abstract

Hypercubes are popular topologies of massive multiprocessor systems due to their super properties. Cross-cubes are significant variations of hypercubes and they have smaller diameters and higher fault-tolerant capability than hypercubes at the same dimensions. In this paper, we construct node-to-set disjoint paths of an n-dimensional cross-cube, \(C_{n}\), whose maximum length is limited by \(2n-3\). Furthermore, we propose an \(O(N \text {log}^{2}N)\) algorithm with a view to finding node-to-set disjoint paths of \(C_{n}\), where N is the node number of \(C_n\). And we also present the simulation results for the maximal length of disjoint paths obtained by our algorithm.

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Acknowledgements

This paper was supported by the National Natural Science Foundation of China (Nos. 61702351 and 61572337), the Joint Found of the National Natural Science Foundation of China (No. U1905211), the Natural Science Foundation of Jiangsu Province (No. BK20180209), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 18KJD520004), the Jiangsu Planned Projects for Postdoctoral Research Funds (No 1701172B), the Fundamental Research Funds for the Central Universities of Jilin University (No 93K172020K25), and the Qing Lan Project of Jiangsu Province.

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Authors and Affiliations

  1. Suzhou Institute of Industrial Technology, Suzhou, 215004, China

    Xi Wang

  2. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Xi Wang, Jianxi Fan & Shukui Zhang

  3. College of Computer Science and Technology, Qingdao University, Qingdao, 266071, China

    Jia Yu

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  1. Xi Wang
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  2. Jianxi Fan
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Correspondence to Shukui Zhang.

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Wang, X., Fan, J., Zhang, S. et al. Node-to-set disjoint paths problem in cross-cubes. J Supercomput 78, 1356–1380 (2022). https://doi.org/10.1007/s11227-021-03872-8

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