A THREE-ROUND ADAPTIVE DIAGNOSTIC ALGORITHM IN A DISTRIBUTED SYSTEM MODELED BY DUAL-CUBES

Abstract

Problem diagnosis in large distributed computer systems and networks is a challenging task that requires fast and accurate inferences from huge volumes of data. In this paper, the PMC diagnostic model is considered, based on the diagnostic approach of end-to-end probing technology. A probe is a test transaction whose outcome depends on some of the system's components; diagnosis is performed by selecting appropriate probes and analyzing the results. In the PMC model, every computer can execute a probe to test a dedicated system's components. Furthermore, any test result reported by a faulty probe station is unreliable and the test result reported by fault-free probe station is always correct. The aim of the diagnosis is to locate all faulty components in the system based on collection of the test results. A dual-cube DC(n) is an (n + 1)-regular spanning subgraph of a (2n + 1)-dimensional hypercube. It uses n-dimensional hypercubes as building blocks and returns the main desirable properties of the hypercube so that it is suitable as a topology for distributed systems. In this paper, we first show that the diagnosability of DC(n) is n + 1 and then show that adaptive diagnosis is possible using at most 22n+1 + n tests for a 22n+1-node distributed system modeled by dual-cubes DC(n) in which at most n + 1 processes are faulty. Furthermore, we propose an adaptive diagnostic algorithm for the DC(n) and show that it diagnoses the DC(n) in three testing rounds and at most 22n+1 + O(n3) tests, where each node is scheduled for at most one test in each round.