The ${\schmi g}$-Good-Neighbor Conditional Diagnosability of ${\schmi k}$-Ary ${\schmi n}$-Cubes under the PMC Modeland MM* Model

Abstract

The diagnosability of a system is defined as the maximum number of faulty processors that the system can guarantee to identify, which plays an important role in measuring of the reliability of multiprocessor systems. In the work of Peng et al. in 2012, they proposed a new measure for fault diagnosis of systems, namely, g-good-neighbor conditional diagnosability. It is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free node contains at least g fault-free neighbors, which can measure the reliability of interconnection networks in heterogeneous environments more accurately than traditional diagnosability. The k-ary n-cube is a family of popular networks. In this study, we first investigate and determine the R g -connectivity of k-ary n-cube for 0 g n: Based on this, we determine the g-good-neighbor conditional diagnosability of k-ary n-cube under the PMC model and MM Ã model for k ! 4; n ! 3 and 0 g n: Our study shows the g-good-neighbor conditional diagnosability of k-ary n-cube is several times larger than the classical diagnosability of k-ary n-cube.

The g-good-neighbor conditional diagnosability of n-dimensional hypercubes under the MM⁎ model

“…In the MM model [5,9], to diagnose a system, a vertex sends the same task to two of its neighbors, and then compares their responses. To be consistent with the MM model, we have the following assumptions.…”

“…Before discussing the g-good-neighbor conditional diagnosability of the n-dimensional hypercube under the MM * model, we first give some useful known theorems. [4,9].) A system G is g-good-neighbor conditional t-diagnosable under the M M * model if and only if for each distinct pair of g-good-neighbor conditional faulty subsets F 1 and F 2 of V with |F 1 | ≤ t and |F 2 | ≤ t satisfies one of the following conditions.…”

“…In [6], they studied the g-good-neighbor conditional diagnosability of the n-dimensional hypercube Q n under PMC model. Later, Yuan et al [9] studied that the g-goodneighbor conditional diagnosability of the k-ary n-cube (k ≥ 4) under the PMC model and MM * model. In this paper, we give that the g-good-neighbor conditional diag-…”

Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults

“…The design of the interconnection network topology significantly determines the performance of the system. A lot of interconnection networks have been proposed in the past decades, for example, hypercube [1] crossed cube [2], twisted cube [3], [4], torus [5], k-ary n-cube [6], [7], [8] and star graph [9]. The k-ary n-cube, denoted by Q k n , is one of the most common interconnection networks due to its desirable properties [10], [11], [12], such as its ability to reduce message latency and ease of implementation.…”

The Tightly Super 3-Extra Connectivity and Diagnosability of Locally Twisted Cubes

“…or Theorem 4.2. ([4,18,20]) A system G = (V, E) is g-extra t-diagnosableunder the MM * model if and only if each distinct pair of g-extra faulty subsets F 1 and F 2 of V with |F 1 | ≤ t and |F 2 | ≤ t satisfies one of the following conditions (seeFig.4):…”