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

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 tr...

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Bibliographic Details
Published inIEEE transactions on parallel and distributed systems Vol. 7; no. 8; pp. 806 - 817
Main Authors Lai, T.H., Ming-Jye Sheng
Format Journal Article
LanguageEnglish
Published Los Alamitos, CA IEEE 01.08.1996
IEEE Computer Society
Subjects
Algorithmics. Computability. Computer arithmetics
Application software
Applied sciences
Computational geometry
Computer science; control theory; systems
Computer Society
Computer systems and distributed systems. User interface
Computer vision
Digital arithmetic
Exact sciences and technology
Image processing
Nearest neighbor searches
Pattern recognition
Software
Software engineering
Sorting
Theoretical computing
Very large scale integration
Computational geometry
Parallel algorithm
Spanning tree
Algorithm complexity
Time complexity
Parallelization
Reconfiguration
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ISSN1045-9219
DOI10.1109/71.532112

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Summary: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 /spl radic/(n/sup 3/)/spl times//spl radic/(n/sup 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/spl times/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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ISSN:1045-9219
DOI:10.1109/71.532112