Abstract
The study of interconnection networks plays an essential role in the design of parallel computing systems because their topological properties make a great impact on the performance and reliability of the systems. The balanced hypercube, designed for fault tolerance, is a variant of the hypercube with desirable properties of strong connectivity, regularity, and symmetry. Over the past decade, the node-disjoint paths problem has received much attention. The existence of these parallel paths can improve reliability, fault tolerance, message throughput, and information security. In this paper, we propose algorithms to construct a maximal number of node-disjoint paths between any two distinct nodes of an n-dimensional balanced hypercube in \(O(n^2)\) time. The lengths of these parallel paths exceed the internode distance by no more than six. In addition, we conduct simulation experiments to evaluate the performance of the fault-tolerant routing using multiple node-disjoint paths as transmission channels.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cheng, D.: The \(h\)-restricted connectivity of balanced hypercubes. Discret. Appl. Math. 305, 133–141 (2021)
Cheng, D., Hao, R.X., Feng, Y.Q.: Two node-disjoint paths in balanced hypercubes. Appl. Math. Comput. 242, 127–142 (2014)
Choudhury, B.S., Das, K.: A new contraction principle in menger spaces. Acta Math. Sin. Engl. Ser. 24(8), 1379–1386 (2008)
Day, K., Tripathi, A.: A comparative study of topological properties of hypercubes and star graphs. IEEE Trans. Parallel Distrib. Syst. 5(1), 31–38 (1994)
Fu, J.S., Chen, G.H., Duh, D.R.: Node-disjoint paths and related problems on hierarchical cubic networks. Netw. Int. J. 40(3), 142–154 (2002)
Guo, C., et al.: Bcube: a high performance, server-centric network architecture for modular data centers. In: Proceedings of the ACM SIGCOMM 2009 Conference on Data Communication, pp. 63–74 (2009)
Hao, R.X., Zhang, R., Feng, Y.Q., Zhou, J.X.: Hamiltonian cycle embedding for fault tolerance in balanced hypercubes. Appl. Math. Comput. 244, 447–456 (2014)
Lai, C.N.: Optimal construction of all shortest node-disjoint paths in hypercubes with applications. IEEE Trans. Parallel Distrib. Syst. 23(6), 1129–1134 (2011)
Latifi, S.: On the fault-diameter of the star graph. Inf. Process. Lett. 46(3), 143–150 (1993)
Liu, H., Cheng, D.: Structure fault tolerance of balanced hypercubes. Theor. Comput. Sci. 845, 198–207 (2020)
Lü, H.: Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges. J. Supercomput. 75, 400–424 (2019)
Lü, H., Wu, T.: Unpaired many-to-many disjoint path cover of balanced hypercubest. Int. J. Found. Comput. Sci. 32(08), 943–956 (2021)
Pai, K.J., Chang, R.S., Chang, J.M.: A protection routing with secure mechanism in möbius cubes. J. Parallel Distrib. Comput. 140, 1–12 (2020)
Pai, K.J., Chang, R.S., Wu, R.Y., Chang, J.M.: Three completely independent spanning trees of crossed cubes with application to secure-protection routing. Inf. Sci. 541, 516–530 (2020)
Wang, G., Lin, C.K., Fan, J., Cheng, B., Jia, X.: A novel low cost interconnection architecture based on the generalized hypercube. IEEE Trans. Parallel Distrib. Syst. 31(3), 647–662 (2019)
Wang, X., Fan, J., Lin, C.K., Jia, X.: Vertex-disjoint paths in DCell networks. J. Parallel Distrib. Comput. 96, 38–44 (2016)
Wei, C., Hao, R.X., Chang, J.M.: The reliability analysis based on the generalized connectivity in balanced hypercubes. Discret. Appl. Math. 292, 19–32 (2021)
Wu, J., Huang, K.: The balanced hypercube: a cube-based system for fault-tolerant applications. IEEE Trans. Comput. 46(4), 484–490 (1997)
Yang, M.C.: Super connectivity of balanced hypercubes. Appl. Math. Comput. 219(3), 970–975 (2012)
Yang, Y.X., Pai, K.J., Chang, R.S., Chang, J.M.: Constructing two completely independent spanning trees in balanced hypercubes. IEICE Trans. Inf. Syst. 102(12), 2409–2412 (2019)
Zhou, J.X., Wu, Z.L., Yang, S.C., Yuan, K.W.: Symmetric property and reliability of balanced hypercube. IEEE Trans. Comput. 64(3), 876–881 (2014)
Zhou, S., Xiao, W., Parhami, B.: Construction of vertex-disjoint paths in alternating group networks. J. Supercomput. 54, 206–228 (2010)
Acknowledgement
This work was supported by the National Natural Science Foundation of China (Nos. 62172291, 62272333) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Liu, S., Wang, Y., Fan, J., Cheng, B. (2024). Node-Disjoint Paths in Balanced Hypercubes with Application to Fault-Tolerant Routing. In: Tari, Z., Li, K., Wu, H. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2023. Lecture Notes in Computer Science, vol 14489. Springer, Singapore. https://doi.org/10.1007/978-981-97-0798-0_3
Download citation
DOI: https://doi.org/10.1007/978-981-97-0798-0_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-0797-3
Online ISBN: 978-981-97-0798-0
eBook Packages: Computer ScienceComputer Science (R0)