174 Int. J. High Performance Computing and Networking, Vol. 4, Nos. 3/4, 2006 Copyright © 2006 Inderscience Enterprises Ltd. A deadlock-free routing algorithm using minimum number of virtual channels and application mappings for Hierarchical Torus Network M.M. Hafizur Rahman* Graduate School of Information Science, 1-1 Asahidai, Tatsunokuchi, Ishikawa-923-1292, Japan E-mail: hafiz90305@yahoo.com *Corresponding author Susumu Horiguchi Graduate School of Information Science, Tohoku University, Aoba 6-3-09, Aramaki, Sendai 980-8579, Japan E-mail: susumu@ecei.tohoku.ac.jp Abstract: A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple Basic Modules (BM), in which the BM are 3D-torus networks that are hierarchically interconnected for higher level networks. In this paper, we present a deadlock-free dimension-order routing using minimum number of Virtual Channels and evaluate the network’s dynamic communication performance under the uniform traffic pattern by computer simulation and compare it with other contemporary conventional and hierarchical networks. We find that the dynamic communication performance of the HTN is better than that of the H3D-mesh, TESH, mesh, and torus networks. We also present the mapping of some primitive applications on the HTN. It is shown that the number of communication steps for various advanced applications mapping on the HTN is lower than that of those networks. Keywords: HTN; wormhole routing; deadlock free routing; uniform traffic patterns; dynamic communication performance; bitonic merge; Fast Fourier Transform (FFT); finding the maximum. Reference to this paper should be made as follows: Rahman, M.M.H. and Horiguchi, S. (2006) ‘A deadlock-free routing algorithm using minimum number of virtual channels and application mappings for Hierarchical Torus Network’, Int. J. High Performance Computing and Networking, Vol. 4, Nos. 3/4, pp.174–187. Biographical notes: M.M. Hafizur Rahman is a PhD student of School of Information Science at JAIST, Japan. Also, he is a research student of Graduate School of Information Science at Tohoku University, Japan. Prior to joining at JAIST, he was a Lecturer at KUET, Bangladesh. He obtained his MSc Degree in information science from the JAIST in 2003. His current research includes interconnection networks, especially hierarchical networks and optical switching networks. Susumu Horiguchi is currently a Full Professor in the GSIS at Tohoku University. Prior to joining in the Tohoku University, he was a Professor at JAIST in Japan, Visiting Professor at University of Southwestern Louisiana and Texas A&M University in USA, and Visiting Scientist at IBM Thomas J. Watson Research Center in USA. He has been involved in organising many international workshops, symposia and conferences sponsored by the IEEE, IEICE and IPS. He is a senior member of the IEEE Computer Society, and a member of the IPS and IASTED. 1 Introduction Interconnection networks are the key elements for building massively parallel computers (Dally, 1990). For computers, with their millions of nodes, the large diameter of conventional topologies is completely infeasible. Hierarchical interconnection networks (Potlapalli, 1995) are a cost-effective way to interconnect a large number of nodes. A variety of hyper-cube based hierarchical interconnection networks have been proposed (Amawy and Latifi, 1991; Esfahanian et al., 1991; Kumar and Patnaik, 1992; Tzeng and Wei, 1991; Ziavras, 1994), but for large scale multicomputer systems, the number of physical links becomes prohibitively large. To alleviate this problem, several k-ary n-cube-based hierarchical interconnection networks: H3D-Mesh (Horiguchi, 1999), H3D-torus (Horiguchi and Ooki, 2000a, 2000b), TESH (Jain et al.,