An introduction to parallel algorithms
Citations
31 citations
Additional excerpts
...As in [ 42 ], the parallel work wp(x, n) denotes the number of operations effectively performed by the algorithm B. We have for all x:...
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31 citations
31 citations
30 citations
Cites background from "An introduction to parallel algorit..."
...Tarjan and Vishkin defined a smaller relation R′c with |R′c|= O(m) and proved that the transitive closure of R′c is the same as that of Rc [20, 12]....
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30 citations
Cites methods or result from "An introduction to parallel algorit..."
...For later reference, we state the following result [ 20 ], [29]....
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...The algorithm is work-time optimal [ 20 ] if it is work-optimal and, in addition, its running time Tp(n) is the best possible among the work-optimal algorithms in that model....
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...For this purpose, we rely, in part, on the following well-known result [ 20 ]....
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...We refer the interested reader to [ 20 ] for an excellent discussion of the PRAM model....
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References
2,895 citations
"An introduction to parallel algorit..." refers background in this paper
...Multiprocessorbased computers have been around for decades and various types of computer architectures [2] have been implemented in hardware throughout the years with different types of advantages/performance gains depending on the application....
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...Every location in the array represents a node of the tree: T [1] is the root, with children at T [2] and T [3]....
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...The text by [2] is a good start as it contains a comprehensive description of algorithms and different architecture topologies for the network model (tree, hypercube, mesh, and butterfly)....
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1,410 citations
"An introduction to parallel algorit..." refers background in this paper
...Parallel architectures have been described in several books (see, for example, [18, 29])....
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1,000 citations
"An introduction to parallel algorit..." refers background in this paper
...Recent work on the mapping of PRAM algorithms on bounded-degree networks is described in [3,13,14, 20, 25], Our presentation on the communication complexity of the matrix-multiplication problem in the sharedmemory model is taken from [1], Data-parallel algorithms are described in [15]....
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951 citations
"An introduction to parallel algorit..." refers background in this paper
...Rigorous descriptions of shared-memory models were introduced later in [11,12]....
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864 citations
"An introduction to parallel algorit..." refers methods in this paper
...The WT scheduling principle is derived from a theorem in [7], In the literature, this principle is commonly referred to as Brent's theorem or Brent's scheduling principle....
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