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$$O(\log \log n)$$-time integer geometry on the CRCW PRAM. (English) Zbl 0837.68121
Summary: We study problems in computational geometry on PRAMs under the assumption that input objects are specified by points with $$O (\log n)$$-bit coordinates, or, equivalently, with polynomially bounded integer coordinates. We show that in this setting many geometric problems can be solved in time $$O (\log \log n)$$. The following five specific problems are investigated: closest pair of points, intersection of convex polygons, intersection of Manhattan line segments, dominating set, and largest empty square. Algorithms solving them are developed which operate in time $$O (\log \log n)$$ on the arbitrary CRCW PRAM. The number of processors used is either $$O(n)$$ or $$O(n \log n)$$.
##### MSC:
 68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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##### References:
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