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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 - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes
IS - 8
SN - 1045-9219
SP806
EP817
EPD - 806-817
A1 - Ten H. Lai,
A1 - Ming-Jye Sheng,
PY - 1996
KW - Parallel algorithms
KW - reconfigurable meshes
KW - computational geometry.
VL - 7
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 

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
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