Triangulation on a Reconfigurable Mesh with Buses

Nigam, M.; Sahni, Sartaj

doi:10.1109/icpp.1994.193

Cited by 6 publications

(2 citation statements)

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“…In this paper, we develop constant time algorithms for computational geometry problems including convex hull, kdimensional maxima, two-set dominance counting, smallest enclosing box, all-pairs nearest neighbor, and triangulation, all on a reconfigurable mesh of size N N. Preliminary versions of this paper have appeared in [11], [30], [31]. Previously, there has been a constant time algorithm for convex hull on a reconfigurable mesh [38].…”

Section: Introductionmentioning

confidence: 99%

Constant time algorithms for computational geometry on the reconfigurable mesh

Jang

Nigam

Prasanna

et al. 1997

IEEE Trans. Parallel Distrib. Syst.

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The reconfigurable mesh consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors. Recently, this model has attracted a lot of attention. In this paper, we show O(1) time solutions to the following computational geometry problems on the reconfigurable mesh: all-pairs nearest neighbors, convex hull, triangulation, two-dimensional maxima, two-set dominance counting, and smallest enclosing box. All these solutions accept N planar points as input and employ an N N reconfigurable mesh. The basic scheme employed in our implementations is to recursively find an O(1) time solution. The number of recursion levels and the size of the subproblems at each level of recursion are optimized such that the problem decomposition and the solution to the problem can be obtained in constant time. As a result, we have developed some efficient merge techniques to combine the solutions for subproblems on the reconfigurable mesh. These techniques exploit reconfigurability in nontrivial ways leading to constant time solutions using optimal size of the mesh.

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Section: Introductionmentioning

confidence: 99%

Constant time algorithms for computational geometry on the reconfigurable mesh

Jang

Nigam

Prasanna

et al. 1997

IEEE Trans. Parallel Distrib. Syst.

Self Cite

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“…Previously, the lower bound was achieved over logn 5 T 5 6 [ 9 ] . Lately, we became aware of results obtained by others using different approaches to solve the subproblems [20,14,13,16 In particular, Madhu after us using Leighton's sort technique which is also used by us.…”

Section: Introductionmentioning

confidence: 99%

An optimal sorting algorithm on reconfigurable mesh

Jang

Prasanna

Proceedings Sixth International Parallel Processing Symposium

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An optimal sorting algorithm on the Reconfigumble Mesh is proposed. The algorithm sorts n numbers in constant time using n x n processors. The best known previous result uses O(n x nlogan) processors. Our algorithm satisfies the AT2 lower bound of for sorting n numbers in the word model of V S Modification to the algorithm for area-time trade-off is shown, to achieve ATa optimality over 1 5 T 5 6. Previously, the bound was achieved over logn 5 T 5 6.

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Computation of the Convex Hull for Sorted Points on a Reconfigurable Mesh

Nakano

1996

Parallel Algorithms and Applications

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Triangulation on a Reconfigurable Mesh with Buses

Cited by 6 publications

References 20 publications

Constant time algorithms for computational geometry on the reconfigurable mesh

Constant time algorithms for computational geometry on the reconfigurable mesh

An optimal sorting algorithm on reconfigurable mesh

Computation of the Convex Hull for Sorted Points on a Reconfigurable Mesh

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