SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM
We show that the Largest Empty Rectangle problem can be solved by reducing it, in a natural way, to the All Nearest Smaller Values problem. We provide two classes of algorithms: the first one assumes that the input points are available sorted by x (resp. y) coordinate. Our algorithm corresponding to this case runs in O(log log n) time using [Formula: see text] processors in the Common-CRCW-PRAM model. For unsorted input, we present algorithms that run in [Formula: see text] time using [Formula: see text] processors in the Common-CRCW-PRAM, or in O( log n) time using [Formula: see text] processors in the EREW-PRAM model. No sub-logarithmic time parallel algorithms have been previously reported for this problem.
1995 ◽
Vol 05
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pp. 273-288
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1997 ◽
Vol 07
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pp. 25-37
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1999 ◽
Vol 10
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pp. 19-31
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1996 ◽
Vol 06
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pp. 213-222
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1988 ◽
Vol 35
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pp. 312-322
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2002 ◽
Vol 12
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pp. 51-64
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1994 ◽
Vol 04
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pp. 437-445
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