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.,