An introduction to parallel algorithms
Citations
40 citations
Additional excerpts
...[8])....
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40 citations
39 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 [27], [24]....
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39 citations
Cites methods from "An introduction to parallel algorit..."
...Consequently, the correctness and the approximation ratio of the algorithm are established by Lemmas 2 and 3. Using standard techniques [ Ja92 ], each iteration of the while loop beginning with q remaining edges can be done in O(ln q) time and O(r q) operations on an EREW-PRAM....
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...Processors. Using standard techniques, the operations can be efficientlyscheduled without increasing the time or the operations by more than a constant, so by the Work-Time Scheduling Principle [ Ja92 ], the number of processors required is M/ln2 m — the work...
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39 citations
Cites background or methods from "An introduction to parallel algorit..."
...See [ 5 , 7] for more background on parallel algorithms....
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...This is possible in O(log n) time using list compression methods (see for example [ 5 ])....
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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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