A Novel Low Cost Interconnection Architecture Based on the Generalized Hypercube

• Published in: IEEE transactions on parallel and distributed systems Vol. 31; no. 3; pp. 647 - 662
• Main Authors: Wang, Guijuan, Lin, Cheng-Kuan, Fan, Jianxi, Cheng, Baolei, Jia, Xiaohua
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Apexes; Architecture; Computer simulation; Construction costs; Cost analysis; Data centers; Diagnosis; disjoint path; Exchanged generalized hypercube; Fault tolerance; Finite element method; Graph theory; Hypercubes; local diagnosis; Low cost; Network topology; Program processors; Routing; Shortest-path problems; Topology
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2019.2941207

The generalized hypercube (GH) is one key interconnection network with excellent topological properties. It contains many other interconnection topologies, such as the hypercube network, the complete graph, the mesh network, and the k-ary n-cube network. It can also be used to construct some data center networks, such as HyperX, BCube, FBFLY, and SWCube. However, the construction cost of GH is high since it contains too many links. In this paper, we propose a novel low cost interconnection architecture called the exchanged generalized hypercube (EGH). We study the properties of EGH, such as the number of edges, the degree of vertices, connectivity, diameter, and diagnosability. Then, we give a routing algorithm to find the shortest path between any two distinct vertices of EGH. Furthermore, we design an algorithm to give disjoint paths between any two distinct vertices of EGH. In addition, we propose two local diagnosis algorithms: LDTEGH and LDWBEGH in EGH under PMC model and MM model, respectively. Simulation results demonstrate that even if the proportion of faulty vertices in EGH is up to 25 percent, the probability that these two diagnosis algorithms can successfully determine the status of vertices is more than 90 percent. As far as the number of edges is concerned, the analysis shows that the construction cost of EGH is much less than that of GH. We could regard this work as the basis for proposing future new high performance topologies.