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The Computer Journal 1993 36(6):562-569; doi:10.1093/comjnl/36.6.562
© 1993 by British Computer Society
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Quadtrees and Hypercubes: Grid Embedding Strategies Based on Spatial Data Structure Addressing

L. A. Breene *

Department of Computer Science, Texas A&M University, TX 77843, USA

A uniform toroidal addressing scheme for k-trees, or spacial data structures, is given. These include bintrees, for decomposing the line, or partitioning linear arrays; quadtrees, for two-dimensional structures; octrees, for three dimensions; etc. Reinterpretation of these addresses as hypercube node identifiers affords simple conceptualization of processor grids of arbitrary Euclidean dimension. Use of gray code produces a hierarchy of topological neighborhoods reflected in the addresses themselves and, with this, fast multicast algorithms for various multiple-processor subgroups.

Received November 2, 1992. revised February 12, 1993.

* Department of Computer Science, Texas A&M University, TX 77843, USA


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