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Sensors 2011, 11(2), 1959-1971; doi:10.3390/s110201959

One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks

1
Department of Computer Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea
2
Department of Information and Communication Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea
3
Department of Information and Communication Engineering, Chosun Universtiy, 375 Seosuk-Dong, Dong-Gu, Gwangju, Korea
*
Author to whom correspondence should be addressed.
Received: 23 November 2010 / Revised: 22 December 2010 / Accepted: 11 January 2011 / Published: 1 February 2011
(This article belongs to the Section Physical Sensors)
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Abstract

As wireless mobile telecommunication bases organize their structure using a honeycomb-mesh algorithm, there are many studies about parallel processing algorithms like the honeycomb mesh in Wireless Sensor Networks. This paper aims to study the Peterson-Torus graph algorithm in regard to the continuity with honeycomb-mesh algorithm in order to apply the algorithm to sensor networks. Once a new interconnection network is designed, parallel algorithms are developed with huge research costs to use such networks. If the old network is embedded in a newly designed network, a developed algorithm in the old network is reusable in a newly designed network. Petersen-Torus has been designed recently, and the honeycomb mesh has already been designed as a well-known interconnection network. In this paper, we propose a one-to-one embedding algorithm for the honeycomb mesh (HMn) in the Petersen-Torus PT(n,n), and prove that dilation of the algorithm is 5, congestion is 2, and expansion is 5/3. The proposed one-to-one embedding is applied so that processor throughput can be minimized when the honeycomb mesh algorithm runs in the Petersen-Torus. View Full-Text
Keywords: embedding; honeycomb mesh; Petersen-Torus; interconnection network parallel processing embedding; honeycomb mesh; Petersen-Torus; interconnection network parallel processing
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MDPI and ACS Style

Seo, J.-H.; Sim, H.; Park, D.-H.; Park, J.-W.; Lee, Y.-S. One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks. Sensors 2011, 11, 1959-1971.

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