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Author Case, John ♦ Rajan, Dayanand S. ♦ Shende, Anil M.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2001
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract In the context of mesh-like, parallel processing computers for (i) approximating continuous space and (ii) $\textit{analog}$ simulation of the motion of objects and waves in continuous space, the present paper is concerned with $\textit{which}$ mesh-like interconnection of processors might be particularly suitable for the task and why. Processor interconnection schemes based on nearest neighbor connections in geometric lattices are presented along with motivation. Then two major threads are exploded regarding which lattices would be good: the regular lattices, for their symmetry and other properties in common with continuous space, and the well-known root lattices, for being, in a sense, the lattices required for physically natural basic algorithms for motion.The main theorem of the present paper implies that thewell-known lattice $A\textit{n}$ is the regular lattice having the maximum number of nearest neighbors among the $\textit{n}-dimensional$ regular lattices. It is noted that the only $\textit{n}-dimensional$ lattices that are both regular and root are $A\textit{n}$ and $Z\textit{n}$ $(Z\textit{n}$ is the lattice of $\textit{n}-cubes.$ The remainder of the paper specifies other desirable properties of $A\textit{n</subscprt}$ including other ways it is superior to $Z\textit{n}$ for our purposes.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2001-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 48
Issue Number 1
Page Count 35
Starting Page 110
Ending Page 144

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Source: ACM Digital Library