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Parallel merge sort
Richard Cole
- 09 Sep 2011
TL;DR: In this paper, a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time is given, and the constant in the running time is small.
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Abstract: We give a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small. We also give a more complex version of the algorithm for the EREW PRAM; it also uses n processors and O(logn) time. The constant in the running time is still moderate, though not as small.
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Citations
Scans as primitive parallel operations
TL;DR: A study of the effects of adding two scan primitives as unit-time primitives to PRAM (parallel random access machine) models is presented and it is shown that the primitives improve the asymptotic running time of many algorithms by an O(log n) factor, greatly simplifying the description of many technologies.
Linear work suffix array construction
TL;DR: A generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space--time tradeoff and is asymptotically faster than all previous suffix tree or array construction algorithms.
481
Parallel computational geometry
TL;DR: In this paper, the authors present efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons, minimizing a circumscribing triangle, and recursive data-structures for three-dimensional queries.
318
•Book
Parallel Computational Geometry
Alok Aggarwal,Bernard Chazelle,Leonidas J. Guibas,Colm Ó'Dúnlaing,Chee Yap +4 more
- 09 Sep 2011
TL;DR: This work presents efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons, minimizing a circumscribing triangle, and recursive data-structures for three-dimensional queries.
238
Parallel symmetry-breaking in sparse graphs
Andrew V. Goldberg,Serge Plotkin,Gregory E. Shannon +2 more
- 01 Jan 1987
TL;DR: Efficient deterministic techniques for breaking symmetry in parallel are described and applied to construct fast linear processor algorithms for several problems, including (&Dgr; + 1)-coloring constant-degree graphs, 5-coloring planar graphs, and finding depth-first-search trees inPlanar graphs.
References
Sorting networks and their applications
Kenneth E. Batcher
- 30 Apr 1968
TL;DR: To achieve high throughput rates today's computers perform several operations simultaneously; not only are I/O operations performed concurrently with computing, but also, in multiprocessors, several computing operations are done concurrently.
Tight bounds on the complexity of parallel sorting
Tom Leighton
- 01 Dec 1984
TL;DR: Tight upper and lower bounds are proved on the number of processors, information transfer, wire area, and time needed to sort N numbers in a bounded-degree fixed-connection network.
239
Searching, Merging, and Sorting in Parallel Computation
TL;DR: A merging algorithm is presented that is optimal up to a constant factor when merging two lists of equal size (independent of the number of processors); as a special case, with N processors it merges two lists, each of size N, in 1.893 lg lg N + 4 comparison steps.
Sorting in c log n parallel steps
TL;DR: A sorting network withcn logn comparisons where in thei-th step of the algorithm the contents of registersRj, andRk, wherej, k are absolute constants then change their contents or not according to the result of the comparison.
Improved upper bounds on shellsort
Janet Incerpi,Robert Sedgewick +1 more
- 07 Nov 1983
TL;DR: The running time of Shellsort, with the number of passes restricted to O(log N), was thought for some time to be Θ(N3/2), but a different approach is used to achieve O(N1+4/√2lgN).
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