Modeling Toroidal Networks with the Gaussian Integers

Carmen Mart&#x00ED;nez; Miquel Moret&#x00F3;; Ernst M. Gabidulin; Ram&#x00F3;n Beivide; Esteban Stafford

doi:10.1109/TC.2008.57

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2008
Issue No. 8 - August
Abstract - Modeling Toroidal Networks with the Gaussian Integers

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	Similar Articles Articles by Carmen Martínez Articles by Ramón Beivide Articles by Esteban Stafford Articles by Miquel Moretó Articles by Ernst M. Gabidulin

Modeling Toroidal Networks with the Gaussian Integers

August 2008 (vol. 57 no. 8)

pp. 1046-1056

	ASCII Text	x
	Carmen Martínez, Ramón Beivide, Esteban Stafford, Miquel Moretó, Ernst M. Gabidulin, "Modeling Toroidal Networks with the Gaussian Integers," IEEE Transactions on Computers, vol. 57, no. 8, pp. 1046-1056, August, 2008.

	BibTex	x
	@article{ 10.1109/TC.2008.57, author = {Carmen Martínez and Ramón Beivide and Esteban Stafford and Miquel Moretó and Ernst M. Gabidulin}, title = {Modeling Toroidal Networks with the Gaussian Integers}, journal ={IEEE Transactions on Computers}, volume = {57}, number = {8}, issn = {0018-9340}, year = {2008}, pages = {1046-1056}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2008.57}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - JOUR JO - IEEE Transactions on Computers TI - Modeling Toroidal Networks with the Gaussian Integers IS - 8 SN - 0018-9340 SP1046 EP1056 EPD - 1046-1056 A1 - Carmen Martínez, A1 - Ramón Beivide, A1 - Esteban Stafford, A1 - Miquel Moretó, A1 - Ernst M. Gabidulin, PY - 2008 KW - Packet-switching networks KW - Network topology KW - Graph theory KW - Graphs and networks KW - Packet routing VL - 57 JA - IEEE Transactions on Computers ER -

Carmen Martínez, University of Cantabria, Santander

Ramón Beivide, University of Cantabria, Santander

Esteban Stafford, University of Cantabria, Santander

Miquel Moretó, UPC UPC , Barcelona Barcelona

Ernst M. Gabidulin, Moscow Institute of Physics and Technology, Moscow

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.57

In this paper we consider a broad family of toroidal networks, denoted as Gaussian networks, which include many previously proposed and used topologies. We will define such networks by means of the Gaussian Integers, the subset of the Complex numbers with integer real and imaginary parts. Nodes in Gaussian networks are labeled by Gaussian integers, which confer these topologies an algebraic structure based on quotient rings of the Gaussian integers. In this sense, Gaussian integers reveal themselves as the appropriate tool for analyzing and exploiting any type of toroidal network. Using this algebraic approach, we can characterize the main distance-related properties of Gaussian networks, providing closed expressions for their diameter and average distance. In addition, we solve some important applications, like unicast and broadcast packet routing or the perfect placement of resources over these networks.

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Index Terms:

Packet-switching networks, Network topology, Graph theory, Graphs and networks, Packet routing

Citation:

Carmen Martínez, Ramón Beivide, Esteban Stafford, Miquel Moretó, Ernst M. Gabidulin, "Modeling Toroidal Networks with the Gaussian Integers," IEEE Transactions on Computers, vol. 57, no. 8, pp. 1046-1056, Aug. 2008, doi:10.1109/TC.2008.57

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