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A lower bound for PARITY on randomized CRCW PRAMs
"... The parity function PARITY(x1 ; : : : ; xn) = P in x i mod 2 is known to be difficult to compute on parallel machines. The famous result of Beame and Hastad says that computing PARITY on PRIORITY CRCW PRAMs requires\Omega\Gamma log n log log n ) steps, provided that the number of processors or ..."
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The parity function PARITY(x1 ; : : : ; xn) = P in x i mod 2 is known to be difficult to compute on parallel machines. The famous result of Beame and Hastad says that computing PARITY on PRIORITY CRCW PRAMs requires\Omega\Gamma log n log log n ) steps, provided that the number of processors
Optimal bounds for decision problems on the CRCW PRAM
 In Proceedings of the 19th ACM Symposium on Theory of Computing (New
"... Abstract. Optimal Q(logn/log logn) lower bounds on the time for CRCW PRAMS with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven. A strict time hierarchy of explicit Boolean functions of n bits on such machines that holds up to ..."
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Cited by 49 (2 self)
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Abstract. Optimal Q(logn/log logn) lower bounds on the time for CRCW PRAMS with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven. A strict time hierarchy of explicit Boolean functions of n bits on such machines that holds up
Abstract Optimal Bounds for Decision Problems on the CRCW PRAM
"... We prove optimal R(log n/log log n) lower bounds on the time for CRCW PRAM’s with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems. We also exhibit a strict time hierarchy of explicit Boolean functions of n bits on such machines which h ..."
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We prove optimal R(log n/log log n) lower bounds on the time for CRCW PRAM’s with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems. We also exhibit a strict time hierarchy of explicit Boolean functions of n bits on such machines which
Retrieval of scattered information by EREW, CREW and CRCW PRAMs
, 1992
"... The kcompaction problem arises when k out of n cells in an array are nonempty and the contents of these cells must be moved to the first k locations in the array. Parallel algorithms for kcompaction have obvious applications in processor allocation and load balancing; kcompaction is also an im ..."
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Cited by 5 (1 self)
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compaction problem requires\Omega\Gammaqui log n) time, even if k = 2. Finally, we show that O(log k) time can be achieved on the ROBUST PRAM, a very weak CRCW PRAM model.
Lower bounds for recognizing small cliques on CRCW PRAM’s
 Discrete Appl. Math
, 1990
"... We show that any CRCW PRAM which recognizes kcliques in nnode graphs in time T requires at least nn(k’r2) processors independent of its memory size. As a corollary we obtain essentially the same tradeoff for unbounded fanin circuits. We also demonstrate a similar but weaker tradeoff for the me ..."
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Cited by 6 (1 self)
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We show that any CRCW PRAM which recognizes kcliques in nnode graphs in time T requires at least nn(k’r2) processors independent of its memory size. As a corollary we obtain essentially the same tradeoff for unbounded fanin circuits. We also demonstrate a similar but weaker trade
On the Power of Some PRAM Models
 Journal of Parallel Algorithms and Applications. Vol
, 1997
"... The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearl ..."
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Cited by 1 (0 self)
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The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n
Comments on Integer Sorting on SumCRCW
"... Abstract Given an array X of n elements from a restricted domain of integers [1, n]. The integer sorting problem is the rearrangement of n integers in ascending order. We study the first optimal deterministic sublogarithmic algorithm for integer sorting on CRCW PRAM. We give two comments on the alg ..."
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Abstract Given an array X of n elements from a restricted domain of integers [1, n]. The integer sorting problem is the rearrangement of n integers in ascending order. We study the first optimal deterministic sublogarithmic algorithm for integer sorting on CRCW PRAM. We give two comments
Parallel Algorithmic Techniques: PRAM Algorithms And PRAM Simulations
, 1995
"... PRAM , which is the Priority CRCW PRAM in which each processor can perform arbitrary complex local operations in a single step. Clearly the Abtract PRAM is stronger than the Priority CRCW PRAM, and actually, it is stronger than any other standard (hence we do not take into account the Minimum CRCW ..."
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PRAM , which is the Priority CRCW PRAM in which each processor can perform arbitrary complex local operations in a single step. Clearly the Abtract PRAM is stronger than the Priority CRCW PRAM, and actually, it is stronger than any other standard (hence we do not take into account the Minimum CRCW
LogP: Towards a Realistic Model of Parallel Computation
, 1993
"... A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding developme ..."
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Cited by 562 (15 self)
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A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding
A simple parallel algorithm for the maximal independent set problem
 SIAM Journal on Computing
, 1986
"... Simple parallel algorithms for the maximal independent set (MIS) problem are presented. The first algorithm is a Monte Carlo algorithm with a very local property. The local property of this algorithm may make it a useful protocol design tool in distributed computing environments and artificial intel ..."
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Cited by 458 (10 self)
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Simple parallel algorithms for the maximal independent set (MIS) problem are presented. The first algorithm is a Monte Carlo algorithm with a very local property. The local property of this algorithm may make it a useful protocol design tool in distributed computing environments and artificial intelligence. One of the main contributions of this paper is the development of powerful and general technicjues for converting Monte Carlo algorithms into deterministic algorithms. These techniques arc used to convert the Monte Carlo algorithm for the MIS problem into a simple deterministic algorithm with the same parallel running time. A maximal independent set (MIS) in an
Results 1  10
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