## Constant Time Algorithms for Computational Geometry on the Reconfigurable Mesh (1997)

Venue: | IEEE Transactions on Parallel and Distributed Systems |

Citations: | 18 - 2 self |

### BibTeX

@ARTICLE{Jang97constanttime,

author = {Ju-wook Jang and Madhusudan Nigam and Viktor K. Prasanna and Sartaj Sahni},

title = {Constant Time Algorithms for Computational Geometry on the Reconfigurable Mesh},

journal = {IEEE Transactions on Parallel and Distributed Systems},

year = {1997},

volume = {8},

pages = {1--12}

}

### OpenURL

### Abstract

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 th...