Broadcastings and digit tilings on three-dimensional torus networks

  • Authors:

  • Ryotaro Okazaki;Hirotaka Ono;Taizo Sadahiro;Masafumi Yamashita

  • Affiliations:

  • Doshisha University, Department of Mathematical Sciences, Kyotanabe, Kyoto, 610-0394, Japan;Kyushu University, Department of Economic Engineering, 6-19-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan;Prefectural University of Kumamoto, 3-1-100 Tsukide, Kumamoto, 862-8502, Japan;Kyushu University, Department of Informatics, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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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) 246-255] to 3-dimensional torus networks.