Publication 1996 Issue No. 8 - August Abstract - Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes
Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes
August 1996 (vol. 7 no. 8)
pp. 806-817
 ASCII Text x Ten H. Lai, Ming-Jye Sheng, "Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 8, pp. 806-817, August, 1996.
 BibTex x @article{ 10.1109/71.532112,author = {Ten H. Lai and Ming-Jye Sheng},title = {Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes},journal ={IEEE Transactions on Parallel and Distributed Systems},volume = {7},number = {8},issn = {1045-9219},year = {1996},pages = {806-817},doi = {http://doi.ieeecomputersociety.org/10.1109/71.532112},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Parallel and Distributed SystemsTI - Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable MeshesIS - 8SN - 1045-9219SP806EP817EPD - 806-817A1 - Ten H. Lai, A1 - Ming-Jye Sheng, PY - 1996KW - Parallel algorithmsKW - reconfigurable meshesKW - computational geometry.VL - 7JA - IEEE Transactions on Parallel and Distributed SystemsER -

Abstract—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 d-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 n points in a fixed d-dimensional space can be constructed in O(1) time on a $\sqrt {n^3}\times \sqrt {n^3}$ R-mesh. Second, all nearest neighbors of n points in a fixed d-dimensional space can be constructed in O(1) time on an n×n R-mesh. There is no previous O(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 d-dimensional space. Both of the proposed algorithms have a time complexity independent of n but growing with d. The time complexity is O(1) if d is a constant.

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Index Terms:
Parallel algorithms, reconfigurable meshes, computational geometry.
Citation:
Ten H. Lai, Ming-Jye Sheng, "Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 8, pp. 806-817, Aug. 1996, doi:10.1109/71.532112