Issue No. 10 - October (1997 vol. 8)

ISSN: 1045-9219

pp: 1019-1035

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.629485

ABSTRACT

<p><b>Abstract</b>—The main contribution of this paper is to present simple and elegant podality-based algorithms for a variety of computational tasks motivated by, and finding applications to, pattern recognition, computer graphics, computational morphology, image processing, robotics, computer vision, and VLSI design. The problems that we address involve computing the convex hull, the diameter, the width, and the smallest area enclosing rectangle of a set of points in the plane, as well as the problems of finding the maximum Euclidian distance between two planar sets of points, and of constructing the Minkowski sum of two convex polygons. Specifically, we show that once we fix a positive constant <tmath>$\epsilon,$</tmath> all instances of size <it>m</it>, <tmath>$\left( {n^{{\textstyle{1 \over 2}}+\epsilon}\le m\le n} \right)$</tmath> of the problems above, stored in the first <tmath>$\left\lceil {{\textstyle{m \over {\sqrt n}}}} \right\rceil $</tmath> columns of a mesh with multiple broadcasting of size <tmath>$\sqrt n\times \sqrt n$</tmath> can be solved time-optimally in <tmath>$\Theta \left( {{\textstyle{m \over {\sqrt n}}}} \right)$</tmath> time.</p>

INDEX TERMS

Podality, pattern recognition, image processing, convex hull, diameter, width, enclosing rectangle, Euclidian distance, Minkowski sum, lower bounds, enhanced meshes, time-optimality.

CITATION

V. Bokka, J. L. Schwing, H. Gurla and S. Olariu, "Podality-Based Time-Optimal Computations on Enhanced Meshes," in

*IEEE Transactions on Parallel & Distributed Systems*, vol. 8, no. , pp. 1019-1035, 1997.

doi:10.1109/71.629485

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