Information Processing Letters 93 (2005) 29–36 www.elsevier.com/locate/ipl Diagnosability of star graphs under the comparison diagnosis model Jun Zheng, Shahram Latifi ∗ , Emma Regentova, Kai Luo, Xiaolong Wu Department of Electrical and Computer Engineering, University of Nevada, Las Vegas, Las Vegas, NV 89154, USA Received 11 March 2003; received in revised form 7 July 2004 Available online 28 October 2004 Communicated by F.B. Schneider Abstract 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.  2004 Elsevier B.V. All rights reserved. Keywords: Diagnosability; Comparison diagnosis model; Star graph; Interconnection networks 1. Introduction Fault-tolerance computing is very important for a multiprocessor system. The first step to deal with faults is to identify the faulty processors from the fault- free ones. The identification process is called the diag- nosis of the system. The diagnosability of the system is defined as a number t such that the system is diag- nosable as long as the number of the faulty processors is not greater than t [3]. Several diagnosis models were proposed to iden- tify the faulty processors. One major approach is the PMC diagnosis model introduced by Preparata et al. [7]. The diagnosis of the system is achieved through two linked processors testing each other. Another ma- * Corresponding author. E-mail address: latifi@unlv.nevada.edu (S. Latifi). jor approach, proposed by Malek and Maeng [6], is called the comparison diagnosis model. The diagno- sis is performed by comparing the responses of pairs of processors to the same input. The comparisons are done by other processors in the system and no cen- tral entity involves. Based on the comparison results, the faulty/fault-free status of the processors can be identified. In [8], the comparison diagnosis model was further studied. A set of criteria was given for deter- mining whether the faulty processors in the system can be diagnosed, and most importantly a polynomial-time algorithm is presented to identify the faulty proces- sors if the system is known to be diagnosable. The di- agnosabilities of hypercube, enhanced hypercube and crossed hypercube under the comparison diagnosis model were studied in [3,9]. The star graph has proved to be a viable candidate for interconnecting the multiprocessor system [1]. The 0020-0190/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ipl.2004.09.011