Circuit-switched row-column broadcasting in torus and mesh networks
This paper is concerned with broadcasting on 2‐dimensional torus and mesh networks using circuit‐switched, half‐duplex, and link‐bound communication. It is assumed that there are α and β physical channels in the X‐ and Y‐dimensions, respectively, and path selection between any two nodes is done usin...
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Published in | Networks Vol. 27; no. 2; pp. 159 - 167 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
Wiley Subscription Services, Inc., A Wiley Company
01.03.1996
John Wiley & Sons |
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Abstract | This paper is concerned with broadcasting on 2‐dimensional torus and mesh networks using circuit‐switched, half‐duplex, and link‐bound communication. It is assumed that there are α and β physical channels in the X‐ and Y‐dimensions, respectively, and path selection between any two nodes is done using row‐column routing. Given an n × n mesh or torus, we first discuss the lower bounds of broadcasting time; any broadcasting algorithm requires at least [log(2α + 2β + 1)n2] time steps and no broadcasting algorithm achieves this lower bound if α < β(2β + 1). We then show that broadcasting on a (2α + 2β + 1)p × (2α + 2β + 1)p torus can be done in 2p time steps, which is optimum, for any α ≥ 3 and β = 1. We also present approximation algorithms for the cases of mesh when α ≥ 1 and β = 1 and torus when α ≤ 2 and β = 1. © 1996 John Wiley & Sons, Inc. |
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AbstractList | This paper is concerned with broadcasting on 2‐dimensional torus and mesh networks using circuit‐switched, half‐duplex, and link‐bound communication. It is assumed that there are α and β physical channels in the X‐ and Y‐dimensions, respectively, and path selection between any two nodes is done using row‐column routing. Given an n × n mesh or torus, we first discuss the lower bounds of broadcasting time; any broadcasting algorithm requires at least [log(2α + 2β + 1)n2] time steps and no broadcasting algorithm achieves this lower bound if α < β(2β + 1). We then show that broadcasting on a (2α + 2β + 1)p × (2α + 2β + 1)p torus can be done in 2p time steps, which is optimum, for any α ≥ 3 and β = 1. We also present approximation algorithms for the cases of mesh when α ≥ 1 and β = 1 and torus when α ≤ 2 and β = 1. © 1996 John Wiley & Sons, Inc. |
Author | Lee Park, Ju-Young Choi, Hyeong-Ah |
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Keywords | Deadlock Approximation Meshed network Optimal algorithm Torus Hypercube Circuit switching Graph theory Information dissemination |
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References | C.-T. Ho and M.-Y. Kao, Efficient broadcast on hypercubes with wormhole and E-cube routings. Technical Report IBM. Parall. Process. Lett., to appear. L. M. Ni and P. K. McKinley, A survey of wormhole routing techniques in direct networks. IEEE Comput. 26 (1993) 62-76. S. M. Hedetniemi, S. T. Hedetniemi, and A. L. Liestman, A survey of gossiping and broadcasting in communication networks. J. Net. 18 (1988) 319-349. J. G. Peters and M. Syska, Circuit-switched broadcasting in torus networks. Technical Report CMPT TR 93-04, School of Computer Science, Simon Fraser University (May 1993). P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks. Discr. Appl. Math. 53 (1994) 79-133. J.-Y. L. Park and H.-A. Choi, Circuit-switched broadcasting in torus and mesh networks. IEEE Trans. Parall. Distrib. Syst., to appear. 1993; 26 1990 1988; 18 1994 1993 1994; 53 |
References_xml | – volume: 53 start-page: 79 year: 1994 end-page: 133 article-title: Methods and problems of communication in usual networks publication-title: Discr. Appl. Math. – volume: 18 start-page: 319 year: 1988 end-page: 349 article-title: A survey of gossiping and broadcasting in communication networks publication-title: J. Net. – article-title: Circuit‐switched broadcasting in torus and mesh networks publication-title: IEEE Trans. Parall. Distrib. Syst. – year: 1990 – volume: 26 start-page: 62 year: 1993 end-page: 76 article-title: A survey of wormhole routing techniques in direct networks publication-title: IEEE Comput. – article-title: Efficient broadcast on hypercubes with wormhole and E‐cube routings publication-title: Technical Report IBM. Parall. Process. Lett. – year: 1993 – year: 1994 – start-page: 288 year: 1993 end-page: 291 |
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SubjectTerms | Applied sciences Exact sciences and technology Switching and signalling Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory |
Title | Circuit-switched row-column broadcasting in torus and mesh networks |
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