The (t, k) -Diagnosability of Balanced Hypercube under the PMC Model

Abstract

ABSTRACTThe network's diagnosability implies its self-diagnostic capability. Compared with classical sequential diagnosis that has been widely used to identify faulty nodes, the -diagnosis is considered as an improvement of sequential diagnosis, where . To be more specific, the -diagnosis can identify and replace at least k faulty nodes in each iteration until all t faulty nodes are found. Meanwhile, compared with the other hypercube graphs, the balanced hypercube (denoted ) has many good properties, such as a better fault-tolerant embedding capability and a smaller diameter. In this paper, we first propose a body discover algorithm (named BD) of , where a body consists of node sets that meet specific conditions. Based on bodies found by BD, we verify that the is -diagnosable. Then we prove that the -diagnosability of is under the PMC model.