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Parallel Prefix Computation
 Journal of the ACM
, 1980
"... ABSTRACT The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recurstve construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fa ..."
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Cited by 333 (1 self)
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ABSTRACT The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recurstve construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields
Probabilistic Parallel Prefix Computation
, 1993
"... Given inputs x,..., xn, which are independent identically distributed random variables over a domain D, and an associative operation o, the probabilistic prefix computation problem is to compute the product x o x2 o .. o xn and its n  1 prefixes. Instances of this problem are finite state transd ..."
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Cited by 1 (0 self)
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Given inputs x,..., xn, which are independent identically distributed random variables over a domain D, and an associative operation o, the probabilistic prefix computation problem is to compute the product x o x2 o .. o xn and its n  1 prefixes. Instances of this problem are finite state
PARALLEL PREFIX COMPUTATION WITH FEW PROCESSORS
, 1992
"... We present a parallel prefix algorithm which uses (2(p + 1)/p (p + 1) + 2) n 1 arithmetic and (p (p 1)/p (p + 1) + 2) n + (1/2) p (p 1) routing steps to compute the prefixes of n elemealta on a distributedmemary multiprocessor with p < n nodes. The algorithm is compared with the distributedm ..."
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Cited by 4 (0 self)
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We present a parallel prefix algorithm which uses (2(p + 1)/p (p + 1) + 2) n 1 arithmetic and (p (p 1)/p (p + 1) + 2) n + (1/2) p (p 1) routing steps to compute the prefixes of n elemealta on a distributedmemary multiprocessor with p < n nodes. The algorithm is compared with the distributed
Parallel Prefix Computation in the Recursive DualNet
"... Abstract. In this paper, we propose an efficient algorithm for parallel prefix computation in recursive dualnet, a newly proposed network. The recursive dualnet RDN k (B) for k> 0 has (2n0) 2k /2 nodes and d0 + k links per node, where n0 and d0 are the number of nodes and the nodedegree of the ..."
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Abstract. In this paper, we propose an efficient algorithm for parallel prefix computation in recursive dualnet, a newly proposed network. The recursive dualnet RDN k (B) for k> 0 has (2n0) 2k /2 nodes and d0 + k links per node, where n0 and d0 are the number of nodes and the node
Optimal Schedules for Parallel Prefix Computation with Bounded Resources
 Proceeding of Third ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
, 1991
"... Given x 1 ; . . . ; xN , parallel prefix computes x 1 ffi x 2 ffi . . . ffi x k , for 1 k N , with associative operation ffi. We show optimal schedules for parallel prefix computation with a fixed number of resources p 2 for a prefix of size N p(p + 1)=2 . The time of the optimal schedules wit ..."
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Cited by 12 (6 self)
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Given x 1 ; . . . ; xN , parallel prefix computes x 1 ffi x 2 ffi . . . ffi x k , for 1 k N , with associative operation ffi. We show optimal schedules for parallel prefix computation with a fixed number of resources p 2 for a prefix of size N p(p + 1)=2 . The time of the optimal schedules
Online adaptive parallel prefix computation
"... Abstract. We consider parallel prefix computation on processors of different and possibly changing speeds. Extending previous works on identical processors, we provide a lower bound for this problem. We introduce a new adaptive algorithm which is based on the online recursive coupling of an optimal ..."
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Cited by 10 (5 self)
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Abstract. We consider parallel prefix computation on processors of different and possibly changing speeds. Extending previous works on identical processors, we provide a lower bound for this problem. We introduce a new adaptive algorithm which is based on the online recursive coupling
DepthSize Tradeoffs for Parallel Prefix Computation
, 1983
"... A prefix circuit has n inputs xi,., x, , and computes the n outputs xi 0... 0 xi, i=l,.., n, where 0 is an associative operation. It is shown that the depth t and the size s of parallel prefix circuits are related by the inequality t + s 2 2n 2. This is true even if arbitrary binary operations can ..."
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A prefix circuit has n inputs xi,., x, , and computes the n outputs xi 0... 0 xi, i=l,.., n, where 0 is an associative operation. It is shown that the depth t and the size s of parallel prefix circuits are related by the inequality t + s 2 2n 2. This is true even if arbitrary binary operations can
Parallel Range Searching in Large Databases Based on General Parallel Prefix Computation
, 2001
"... this paper, we first present a computation and communication optimal parallel GPC algorithm on a general purpose parallel programming model, CGM (Coarse Grained Multicomputers, [2]). A CGM computer consists of p processors P 0 ; \Delta \Delta \Delta P p\Gamma1 , where each processor has O( p ) loca ..."
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this paper, we first present a computation and communication optimal parallel GPC algorithm on a general purpose parallel programming model, CGM (Coarse Grained Multicomputers, [2]). A CGM computer consists of p processors P 0 ; \Delta \Delta \Delta P p\Gamma1 , where each processor has O( p
Pipelined Parallel Prefix Computations, and Sorting on a Pipelined Hypercube
 Journal of Parallel and Distributed Computing
, 1993
"... This paper brings together a number of previously known techniques in order to obtain practical and efficient implementations of the prefix operation for the complete binary tree, hypercube and shuffle exchange families of networks. For each of these networks, we also provide a "pipelined&qu ..."
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Cited by 14 (7 self)
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This paper brings together a number of previously known techniques in order to obtain practical and efficient implementations of the prefix operation for the complete binary tree, hypercube and shuffle exchange families of networks. For each of these networks, we also provide a "
Matrix exponentials and parallel prefix computation in a quantum control problem
"... Quantum control plays a key role in quantum technology, in particular for steering quantum systems. As problem size grows exponentially with the system size, it is necessary to deal with fast numerical algorithms and implementations. We improved an existing code for quantum control concerning two l ..."
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that the Chebyshev method outperforms the other methods both in terms of computation time and accuracy. For the prefix problem we compare the treebased parallel prefix scheme, which is based on a recursive approach, with a sequential multiplication scheme where only the individual matrix multiplications
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