<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.</p></abstract>

Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Graduate School of Science, Kanagawa University, Tsuchiya 2946, Hiratsuka, Kanagawa, 259-1293 Japan

Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo, 184-8588 Japan

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other....

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Published Online: Dec 30, 2015

Page range: 723 - 735

Received: Apr 09, 2014

DOI: https://doi.org/10.1515/amcs-2015-0052

Keywords
algorithm, routing, Hamiltonian, supercomputer, parallel

© 2015 Antoine Bossard et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Published Online: Dec 30, 2015

Page range: 723 - 735

Received: Apr 09, 2014

DOI: https://doi.org/10.1515/amcs-2015-0052

Keywordsalgorithm, routing, Hamiltonian, supercomputer, parallel

© 2015 Antoine Bossard et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
algorithm, routing, Hamiltonian, supercomputer, parallel