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.
Highlights
Computers are widely used in our everyday life
The processor throughput could be minimized through one-to-one embedding
Further studies on embedding from Petersen-Torus in other interconnection networks are required to be made so that the algorithms developed in Petersen-Torus can be reusable in another interconnection network
Summary
Computers are widely used in our everyday life. Almost all computers have one processor that is able to perform instructions sequentially. Since a low dimension mesh can be readily designed and is very useful in terms of algorithm, it is frequently used as interconnection network for parallel computers. The measures to evaluate the embedding algorithm are dilation, congestion, and expansion. Message transfer in multi-computing system is divided into circuit switching and packet switching The former makes two processors exclusively available while transferring message by setting circuits toward the destination. In [26], k-dimensional Torus G was embedded in H at dilation 1 and congestion 1(If the number of nodes of G is equivalent to or more than that of H). Torus was embedded in n-dimensional hexagonal honeycomb Torus at dilation 2, congestion 4, expansion 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
