Abstract
Based on Petersen graph, a new interconnection network, the RP(k) network, is developed and the properties of the RP(k) network are investigated. The diameter of the RP(k) network is [k/2] + 2 and its degree is 5. We prove that the diameter of the RP(k) network is much smaller than that of the 2-D Torus network when the number of nodes in interconnection networks is less than or equal to 300. In order to analyze the communication performance in a group of nodes, we propose the concepts of the optimal node groups and the diameter of the optimal node groups. We also show that the diameter of the optimal node groups in the RP(k) network is less than that in the 2-D Torus network. Especially when the number of nodes in an optimal node group is between 6 and 100, the diameter of the optimal node groups in the RP(k) network is half of that in the 2-D Torus network. Furthermore based on the RP(k) network we design a set of routing algorithms which are point-to-point routing, permutation routing, one-to-all routing and all-to-all routing. Their communication efficiencies are [k/2] + 2,k + 5, [k/2] + 2, andk + 5 respectively. The RP(k) network and the routing algorithms can provide efficient communication means for parallel and distributed computer system.
Similar content being viewed by others
References
Chen, G. H., Duh, D. R., Topological properties, communication, and computation on WK-recursive networks, Networks, 1994, 24(6): 303–317.
Su Ming-Ying, Chen Gen-Huey, Duh Dyi-Rong, Broadcasting on incomplete WK-recursive networks, Journal of Parallel and Distributed Computing, 1999, 57: 217–224.
Fen Lin Wu, Lakshmivarahan, S., Dhall, S. K., Routing in a class of cayley graphs of semidirect products of finite groups, Journal of Parallel and Distributed Computing, 2000, 60: 539–565.
Lakshmivarahan, S., Dhall, S. K., Ring, torus and hypercube architectures/algorithms for parallel computing, Parallel Computing, 1999, 25: 1877–1906.
Zheng, S. Q., Wu Jie, Dual of a complete graph as an interconnection network, Journal of Parallel and Distributed Computing, 2000, 60: 1028–1046.
Femandes, R., Kanevsky, A., Generalized ring interconnection networks, The Proceedings of 1994 International Conference on Parallel Processing, IEEE, 1994, 30–34.
Xu Jin, Self-Complementary Graph Theory with Application (in Chinese), Xi’an: Publishing House of Xi’an Electrical and Scientific University, 1999.
Das, S. K., Ohring, S., Baneriee, A. K., Hyper Petersen network: Yet another hypercube-like topology, The Fourth Symposium on the Frontiers of Massively Parallel Computation, McLean Vir., 1992, 270–277.
Yeh, Chi-Hsiang, Parhami, B., Routing and embeddings in cyclic Petersen network: an efficient extension of the Petersen graph, Proc. Int’l Conf. Parallel Processing, IEEE, Japan, Sep. 1999, 258–265.
Siegel, H. J., Interconnection Networks for Large-scale Parallel Processing, New York: McGraw-Hill Publishing Company, 1990.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, F., Liu, Z. & Qiao, X. A practical interconnection network RP(k) and its routing algorithms. Sci China Ser F 44, 461–473 (2001). https://doi.org/10.1007/BF02713950
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02713950