Comparison Diagnosis Model Research Articles

COMPARISON-BASED CONDITIONAL DIAGNOSABILITY ON THE CLASS OF HYPERCUBE-LIKE NETWORKS

For system diagnosis, Lai et al.16 introduced a new measurement, called the conditional diagnosability, by adding a condition that no faulty set contains all the neighbors of any vertex in a network. Taking the hypercube as the target, Lai et al.16 (respectively, Hsu et al.13) estimated the PMC-based19 (respectively, the comparison-based18) conditional diagnosability as about four (respectively, three) times larger than the original diagnosability. In this paper, we extend the concept of conditional diagnosability to the generalized version of hypercubes, the class of hypercube-like networks. We prove that the conditional diagnosability of an n-dimensional hypercube-like network HLn is 3n - 5 under the comparison diagnosis model, for n ≥ 5.

Using Node Diagnosability to Determine t-Diagnosability under the Comparison Diagnosis Model

Diagnosis is an essential subject for the reliability of a multiprocessor system. Under the comparison diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity O(N5) to identify all the faulty processors for a given syndrome in a system with N processors. In this paper, we present a novel idea on system diagnosis called node diagnosability. The node diagnosability can be viewed as a local strategy toward system diagnosability. There is a strong relationship between the node diagnosability and the traditional diagnosability. For this local sense, we focus more on a single processor and require only identifying the status of this particular processor correctly. Under the comparison diagnosis model, we propose a sufficient condition to determine the node diagnosability of a given processor. Furthermore, we propose a useful local structure called an extended star to guarantee the node diagnosability and provide an efficient algorithm to determine the faulty or fault-free status of each processor based on this structure. For a multiprocessor system with total number of processors N, the time complexity of our algorithm to diagnose a given processor is O(\log N) and that to diagnose all the faulty processors is O(N\log N) under the comparison model, provided that there is an extended star structure at each processor and that the time for looking up the testing result of a comparator in the syndrome table is constant.

Strongly Diagnosable Systems under the Comparison Diagnosis Model

A system is t-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed t, where t is some positive integer. Furthermore, a system is strongly t-diagnosable if it is t-diagnosable and can achieve (t+1)-diagnosable except for the case where a node's neighbors are all faulty. In this paper, we propose some conditions for verifying whether a class of interconnection networks, called matching composition networks (MCNs), are strongly diagnosable under the comparison diagnosis model.

Conditional diagnosability of hypercubes under the comparison diagnosis model

Processor fault diagnosis plays an important role in multiprocessor systems for reliable computing, and the diagnosability of many well-known networks has been explored. Lai et al. proposed a novel measure of diagnosability, called conditional diagnosability, by adding an additional condition that any faulty set cannot contain all the neighbors of any vertex in a system. We make a contribution to the evaluation of diagnosability for hypercube networks under the comparison model and prove that the conditional diagnosability of n -dimensional Hypercube Q n is 3( n − 2) + 1 for n ⩾ 5. The conditional diagnosability of Q n is about three times larger than the classical diagnosability of Q n .

Strongly Diagnosable Product Networks Under the Comparison Diagnosis Model

The notion of diagnosability has long played an important role in measuring the reliability of multiprocessor systems. Such a system is t-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed t, where t is some positive integer. Furthermore, a system is strongly i-diagnosable if it can achieve (t + 1)-diagnosability, except for the case where a node's neighbors are all faulty. In this paper, we investigate the strong diagnosability of a class of product networks, under the comparison diagnosis model. Based on our results, we can determine the strong diagnosability of several widely used multiprocessor systems, such as hypercubes, mesh-connected k-ary n-cubes, torus-connected k-ary n-cubes, and hyper-Petersen networks.

PMC 모델과 비교진단 모델을 이용한 하이퍼-스타 연결망의 진단도 분석

진단도는 상호연결망의 신뢰도를 측정하는 중요한 요소 중 하나이다. 고장 노드를 진단하기 위한 대표적인 모델로 PMC 모델과 비교진단 모델이 있다. 본 논문에서는 두 모델을 이용하여 정규연결망 하이퍼-스타 HS(2n,n)의 진단도(Diagnosability)가 n임을 보인다. Diagnosability is an important factor in measuring the reliability of an interconnection network. Typical models of fault diagnosis are the PMC and the comparison diagnosis model. In this paper, we prove that the regular network Hyper-Star HS(2n,n) under two models is n-diagnosable.

Diagnosability of t-connected networks and product networks under the comparison diagnosis model

Diagnosability is an important factor in measuring the reliability of an interconnection network, while the (node) connectivity is used to measure the fault tolerance of an interconnection network. We observe that there is a close relationship between the connectivity and the diagnosability. According to our results, a t-regular and t-connected network with at least 2t + 3 nodes is t-diagnosable. Furthermore, the diagnosability of the product networks is also investigated in this work. The product networks, including hypercube, mesh, and tori, comprise very important classes of interconnection networks. Herein, different combinations of t-diagnosable and t-connected are employed to study the diagnosability of the product networks.

Diagnosability of star graphs under the comparison diagnosis model

In this paper, the diagnosability of n-dimensional star graph S n under the comparison diagnosis model has been studied. It is proved that S n is ( n − 1 ) -diagnosable under the comparison diagnosis model when n ⩾ 4 .

The diagnosability of the matching composition network under the comparison diagnosis model

The classical problem of diagnosability is discussed widely and the diagnosability of many well-known networks has been explored. We consider the diagnosability of a family of networks, called the matching composition network (MCN); a perfect matching connects two components. The diagnosability of MCN under the comparison model is shown to be one larger than that of the component, provided some connectivity constraints are satisfied. Applying our result, the diagnosability of the hypercube Qn, the crossed cube CQ/sub n/, the twisted cube TQ/sub n/, and the Mobius cube MQ/sub n/ can all proven to be n, for n/spl ges/4. In particular, we show that the diagnosability of the four-dimensional hypercube Q/sub 4/ is 4, which is not previously known.

Diagnosability of crossed cubes under the comparison diagnosis model

Diagnosability of crossed cubes under the comparison diagnosis model

Diagnosability of crossed cubes under the comparison diagnosis model

Diagnosability of a multiprocessor system is one important study topic in the parallel processing area. As a hypercube variant, the crossed cube has many attractive properties. The diameter, wide diameter and fault diameter of it are all approximately half of those of the hypercube. The power that the crossed cube simulates trees and cycles is stronger than the hypercube. Because of these advantages of the crossed cube, it has attracted much attention from researchers. We show that the n-dimensional crossed cube is n-diagnosable under a major diagnosis model-the comparison diagnosis model proposed by Malek (1980) and Maeng and Malek (1981) if n/spl ges/4. According to this, the polynomial algorithm presented by Sengupta and Dahbura (1992) may be used to diagnose the n-dimensional crossed cube, provided that the number of the faulty nodes in the n-dimensional crossed cube does not exceed n. The conclusion of this paper also indicates that the diagnosability of the n-dimensional crossed cube is the same as that of the n-dimensional hypercube when n>5 and better than that of the n-dimensional hypercube when n=4.

Diagnosability of hypercubes and enhanced hypercubes under the comparison diagnosis model

A. Sengupta and A. Dahbura (1992) discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by J. Maeng and M. Malek (1981) and a polynomial algorithm was given to identify the faulty processors provided that the system's diagnosability is known. However, for a general system, the determination of its diagnosability is not algorithmically easy. This paper proves that, for the important hypercube structured multiprocessor systems (n-cubes), the diagnosability under the comparison model is n when n/spl ges/5. The paper also studies the diagnosability of enhanced hypercube, which is obtained by adding 2/sup n-1/ more links to a regular hypercube of 2/sup n/ processors. It is shown that the augmented communication ability among processors also increases the system's diagnosability under the comparison model. We prove that the diagnosability is n+1 for an enhanced hypercube when n/spl ges/6.