Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Locality, communication, and interconnect length in multicomputers
SIAM Journal on Computing
Digital analog simulation of uniform motion in representations of physical N-space by lattice-work MIMD computer architectures
A characterization of root lattices
Discrete Mathematics
Parallel Integrated Technology for Image Processing
Parallel Integrated Technology for Image Processing
Readings in Knowledge Representation
Readings in Knowledge Representation
Multicomputers and Image Processing: Algorithms and Programs; Based on a Symposium Held in Madison, WISC., May 26-29, 1981
Wireless ad hoc lattice computers (WAdL)
Journal of Parallel and Distributed Computing - Special issue: Algorithms for wireless and ad-hoc networks
Digital hyperplane recognition in arbitrary fixed dimension within an algebraic computation model
Image and Vision Computing
Proxy assignments for filling gaps in wireless ad-hoc lattice computers
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
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In the context of mesh-like, parallel processing computers for (i) approximating continuous space and (ii) analog simulation of the motion of objects and waves in continuous space, the present paper is concerned with 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 An is the regular lattice having the maximum number of nearest neighbors among the n-dimensional regular lattices. It is noted that the only n-dimensional lattices that are both regular and root are An and Zn (Zn is the lattice of n-cubes. The remainder of the paper specifies other desirable properties of An including other ways it is superior to Zn for our purposes.