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Constructing Euclidean minimum spanning trees and all nearest neighbors on reconfigurable meshes

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2 Author(s)
Lai, T.H. ; Dept. of Comput. & Inf. Sci., Ohio State Univ., Columbus, OH, USA ; Ming-Jye Sheng

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 √(n3)×√(n3) 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

Published in:

Parallel and Distributed Systems, IEEE Transactions on  (Volume:7 ,  Issue: 8 )

Date of Publication:

Aug 1996

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