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ABSTRACT
<p><b>Abstract</b>—A reconfigurable mesh, R-mesh for short, is a two-dimensional array of processors connected by a grid-shaped reconfigurable bus system. Each processor has four I/O ports that can be locally connected during execution of algorithms. This paper considers the <it>d</it>-dimensional Euclidean Minimum Spanning Tree (EMST) and the All Nearest Neighbors (ANN) problem. Two results are reported. First, we show that a minimum spanning tree of <it>n</it> points in a fixed <it>d</it>-dimensional space can be constructed in <it>O</it>(1) time on a <tmath>$\sqrt {n^3}\times \sqrt {n^3}$</tmath> R-mesh. Second, all nearest neighbors of <it>n</it> points in a fixed <it>d</it>-dimensional space can be constructed in <it>O</it>(1) time on an <it>n</it>×<it>n</it> R-mesh. There is no previous <it>O</it>(1) time algorithm for the EMST problem; ours is the first such algorithm. A previous R-mesh algorithm exists for the two-dimensional ANN problem; we extend it to any <it>d</it>-dimensional space. Both of the proposed algorithms have a time complexity independent of <it>n</it> but growing with <it>d</it>. The time complexity is <it>O</it>(1) if <it>d</it> is a constant.</p>
INDEX TERMS
Parallel algorithms, reconfigurable meshes, computational geometry.
CITATION

M. Sheng and T. H. Lai, "Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes," in IEEE Transactions on Parallel & Distributed Systems, vol. 7, no. , pp. 806-817, 1996.
doi:10.1109/71.532112
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