## Ultra-fast expected time parallel algorithms (1991)

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Venue: | Proc. of the 2nd SODA |

Citations: | 20 - 3 self |

### BibTeX

@INPROCEEDINGS{Mackenzie91ultra-fastexpected,

author = {Philip D. Mackenzie and Quentin F. Stout},

title = {Ultra-fast expected time parallel algorithms},

booktitle = {Proc. of the 2nd SODA},

year = {1991},

pages = {414--423}

}

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### Abstract

It has been shown previously that sorting n items into n locations with a polynomial number of processors requires Ω(log n/log log n) time. We sidestep this lower bound with the idea of Padded Sorting, or sorting n items into n + o(n) locations. Since many problems do not rely on the exact rank of sorted items, a Padded Sort is often just as useful as an unpadded sort. Our algorithm for Padded Sort runs on the Tolerant CRCW PRAM and takes Θ(log log n/log log log n) expected time using n log log log n/log log n processors, assuming the items are taken from a uniform distribution. Using similar techniques we solve some computational geometry problems, including Voronoi Diagram, with the same processor and time bounds, assuming points are taken from a uniform distribution in the unit square. Further, we present an Arbitrary CRCW PRAM algorithm to solve the Closest Pair problem in constant expected time with n processors regardless of the distribution of points. All of these algorithms achieve linear speedup in expected time over their optimal serial counterparts. 1 Research done while at the University of Michigan and supported by an AT&T Fellowship.