Circuit-switched row-column broadcasting in torus and mesh networks

• Published in: Networks Vol. 27; no. 2; pp. 159 - 167
• Main Authors: Lee Park, Ju-Young, Choi, Hyeong-Ah
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.03.1996; John Wiley & Sons
• Subjects: Applied sciences; Exact sciences and technology; Switching and signalling; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Deadlock; Approximation; Meshed network; Optimal algorithm; Torus; Hypercube; Circuit switching; Graph theory; Information dissemination
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/(SICI)1097-0037(199603)27:2<159::AID-NET7>3.0.CO;2-J

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.