### Abstract

A tiling in a finite abelian group H is a pair (T,L) of subsets of H such that any h∈H can be uniquely represented as t+l where t∈T and l∈L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem of broadcasting on circuit switched networks. We extend the tiling argument of Peters and Syska [Joseph G. Peters, Michel Syska, Circuit switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 246255] to 3-dimensional torus networks.

Original language | English |
---|---|

Pages (from-to) | 307-319 |

Number of pages | 13 |

Journal | Theoretical Computer Science |

Volume | 412 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - Feb 4 2011 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*412*(4-5), 307-319. https://doi.org/10.1016/j.tcs.2010.09.028

**Broadcastings and digit tilings on three-dimensional torus networks.** / Okazaki, Ryotaro; Ono, Hirotaka; Sadahiro, Taizo; Yamashita, Masafumi.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 412, no. 4-5, pp. 307-319. https://doi.org/10.1016/j.tcs.2010.09.028

}

TY - JOUR

T1 - Broadcastings and digit tilings on three-dimensional torus networks

AU - Okazaki, Ryotaro

AU - Ono, Hirotaka

AU - Sadahiro, Taizo

AU - Yamashita, Masafumi

PY - 2011/2/4

Y1 - 2011/2/4

N2 - A tiling in a finite abelian group H is a pair (T,L) of subsets of H such that any h∈H can be uniquely represented as t+l where t∈T and l∈L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem of broadcasting on circuit switched networks. We extend the tiling argument of Peters and Syska [Joseph G. Peters, Michel Syska, Circuit switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 246255] to 3-dimensional torus networks.

AB - A tiling in a finite abelian group H is a pair (T,L) of subsets of H such that any h∈H can be uniquely represented as t+l where t∈T and l∈L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem of broadcasting on circuit switched networks. We extend the tiling argument of Peters and Syska [Joseph G. Peters, Michel Syska, Circuit switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 246255] to 3-dimensional torus networks.

UR - http://www.scopus.com/inward/record.url?scp=78650841109&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650841109&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2010.09.028

DO - 10.1016/j.tcs.2010.09.028

M3 - Article

AN - SCOPUS:78650841109

VL - 412

SP - 307

EP - 319

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 4-5

ER -