The use of the star graph as a viable interconnection scheme for parallel computers has been examined by a number of authors in recent times. An attractive feature of this class of graphs is that it has sublogarithmic diameter and has a great deal of symmetry akin to the binary hypercube. In this paper we describe a new class of algorithms for embedding (a) Hamiltonian cycle (b) the set of all even cycles and (c) a variety of two- and multi-dimensional grids in a star graph. In addition, we also derive an algorithm for the ranking and the unranking problem with respect to the Hamiltonian cycle.
This paper introduces a new class of interconnection scheme based on the Cayley graph of the alternating group. It is shown that this class of graphs are edge symmetric and 2-transitive. We then describe an algorithm for (a) packet routing based on the shortest path analysis, (b) finding a Hamiltonian cycle, (c) ranking and unranking along the chosen Hamiltonian cycle, (d) unit expansion and dilation three embedding of a class of two-dimensional grids, (e) unit dilation embedding of a variety of cycles, and (f) algorithm for broadcasting messages. The paper concludes with a short analysis of contention resulting from a typical communication scheme. Although this class of graphs does not possess many of the symmetry properties of the binary hypercube, with respect to the one source broadcasting, these graphs perform better than does a hypercube, and with respect to the contention problem, these graphs perform better than do the star graphs and are close to the hypercube. 0 1993 by John Wiley & Sons, Inc.
Immediate monitoring of the conditions of the grinding wheel during the grinding process is important because it directly affects the surface accuracy of the workpiece. Because the variation in machining sound during the grinding process is very important for the field operator to judge whether the grinding wheel is worn or not, this study applies artificial intelligence technology to attempt to learn the experiences of auditory recognition of experienced operators. Therefore, we propose an intelligent system based on machining sound and deep learning to recognize the grinding wheel condition. This study uses a microphone embedded in the grinding machine to collect audio signals during the grinding process, and extracts the most discriminated feature from spectrum analysis. The features will be input the designed CNNs architecture to create a training model based on deep learning for distinguishing different conditions of the grinding wheel. Experimental results show that the proposed system can achieve an accuracy of 97.44%, a precision of 98.26% and a recall of 96.59% from 820 testing samples. INDEX TERMS Grinding wheel wear, intelligent system, machining sound, audio signals, deep learning. I. INTRODUCTION CHENG-HSIUNG LEE received the B.I.M. and M.I.M. degrees in information management from the Chaoyang University of Technology, in 2002 and 2004, respectively, and the Ph.D. degree in computer science and engineering from the
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