The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.
The design of interconnection networks is a fundamental aspect of high-performance computing (HPC) systems. Among the available topologies, the Galaxyfly network stands out as a low-diameter and flexible-radix network for HPC applications. Given the paramount importance of collective communication in HPC performance, in this paper, we present two different all-to-all broadcast algorithms for the Galaxyfly network, which adhere to the supernode-first rule and the router-first rule, respectively. Our performance evaluation validates their effectiveness and shows that the first algorithm has a higher degree of utilization of network channels, and that the second algorithm can significantly reduce the average time for routers to collect packets from the supernode.
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