Characterization of component diagnosability of regular networks

Abstract

Multiprocessor systems, which usually take interconnection network (or graph) as underlying topologies, are commonly deployed for big data analysis because of evolution in technologies such as cloud computing, IoT, social network and so on. Reliability evaluation is of significant importance to characterize fault tolerability for the topologies of multiprocessor systems, and system-level diagnosis is a primary strategy to identify the faulty processors in the systems. The g-component connectivity cκg(G) of a graph G is the size of a minimal vertex-set, whose removal will disconnect G to possess at least g components, which reflects the invulnerability of the topology graph. Based on g-component connectivity of graph G, the g-component diagnosability ctg(G) of regular networks has been proposed as a parameter to measure network fault-tolerability. The g-component diagnosability ctg(G) is the maximum t such that the graph G is g-component t-diagnosable. We first propose some general characterizations of the component diagnosability of regular networks under the classic PMC model and MM∗ model based on the component connectivity. And then we present some empirical analysis for some kinds of well-known regular networks, such as BC networks, star graphs, bubble-sort star graphs, alternating group graphs.