# Torus-connected cycles: A simple and scalable topology for interconnection networks

Antoine Bossard; Keiichi Kaneko

International Journal of Applied Mathematics and Computer Science (2015)

- Volume: 25, Issue: 4, page 723-735
- ISSN: 1641-876X

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topAntoine Bossard, and Keiichi Kaneko. "Torus-connected cycles: A simple and scalable topology for interconnection networks." International Journal of Applied Mathematics and Computer Science 25.4 (2015): 723-735. <http://eudml.org/doc/275991>.

@article{AntoineBossard2015,

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.},

author = {Antoine Bossard, Keiichi Kaneko},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {algorithm; routing; Hamiltonian; supercomputer; parallel},

language = {eng},

number = {4},

pages = {723-735},

title = {Torus-connected cycles: A simple and scalable topology for interconnection networks},

url = {http://eudml.org/doc/275991},

volume = {25},

year = {2015},

}

TY - JOUR

AU - Antoine Bossard

AU - Keiichi Kaneko

TI - Torus-connected cycles: A simple and scalable topology for interconnection networks

JO - International Journal of Applied Mathematics and Computer Science

PY - 2015

VL - 25

IS - 4

SP - 723

EP - 735

AB - 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.

LA - eng

KW - algorithm; routing; Hamiltonian; supercomputer; parallel

UR - http://eudml.org/doc/275991

ER -

## References

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