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New lower bounds for parallel computation

Ming Li, Yaacov Yesha
1989 Journal of the ACM  
However, for the case of polynomially many processors, this upper bound is more than a polynomial in n. (2) An R(log n) lower bound is given for PRIORITY(m) with no"' processors on a function with inputs  ...  Lower bounds are proven on the parallel-time complexity of several basic functions on the most powerful concurrent-read concurrent-write PRAM with unlimited shared memory and unlimited power of individual  ...  We thank Eitan Gurari, Xin He, and Tim Long for their generous help, and the anonymous referees for very helpful suggestions.  ... 
doi:10.1145/65950.65959 fatcat:3ehin4j34vb65hnyqu22jvrlbq

New lower bounds for Massively Parallel Computation from query complexity [article]

Moses Charikar, Weiyun Ma, Li-Yang Tan
2020 arXiv   pre-print
Roughgarden, Vassilvitskii, and Wang (JACM 18) recently introduced a novel framework for proving lower bounds for Massively Parallel Computation using techniques from boolean function complexity.  ...  In addition to strengthening the connections between Massively Parallel Computation and boolean function complexity, we also develop new machinery to reason about the latter.  ...  Acknowledgments We thank Jakub Łącki and the co-authors of [BDE + 19b] for clarifications on the AMPC model and valuable feedback on our specifications of the model.  ... 
arXiv:2001.01146v1 fatcat:vdxo3c7jfnh47axdwxfstheluu

New algorithms and lower bounds for the parallel evaluation of certain rational expressions

H. T. Kung
1974 Proceedings of the sixth annual ACM symposium on Theory of computing - STOC '74  
Similar algorithms for the evaluation of other polynomial expressions are also introduced. Lower bounds on the time needed for the parallel evaluation of rational expressions are given.  ...  This paper presents new algorithms for the parallel evaluation of certain polynomial expressions.  ...  If division is not used I [log n]M is a lower bound on the time for the parallel evaluation of n x , no matter how many processors are used.  ... 
doi:10.1145/800119.803911 dblp:conf/stoc/Kung74 fatcat:lv2pb56mjncdbh6kcs2w6qf4ly

Introduction [chapter]

Andrea Pietracaprina, Rob Bisseling, Emmanuelle Lebhar, Alexander Tiskin
2009 Lecture Notes in Computer Science  
The result generalizes a known lower bound for d = 3.  ...  The second paper, A Lower Bound for Oblivious Dimensional Routing, by A.  ...  The second paper, A Lower Bound for Oblivious Dimensional Routing, by A.  ... 
doi:10.1007/978-3-642-03869-3_90 fatcat:4wq3w5zeyjgkvgxokqo3dqcjry

Parallel Branch and Bound on a CPU-GPU System

Abdelamine Boukedjar, Mohamed Esseghir Lalami, Didier El-Baz
2012 2012 20th Euromicro International Conference on Parallel, Distributed and Network-based Processing  
Hybrid implementation via CUDA of a branch and bound method for knapsack problems is proposed.  ...  Branch and bound computations can be carried out either on the CPU or on the GPU according to the size of the branch and bound list, i.e. the number of nodes.  ...  Acknowledgment Dr Didier El Baz would like to thank NVIDIA for his support through Academic Partnership.  ... 
doi:10.1109/pdp.2012.23 dblp:conf/pdp/BoukedjarLB12 fatcat:g24wq6bqibcnpcnd2kgyz3pk4i

Page 5448 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
n))-lower bounds for Andreev’s function, which is now the largest lower bound for the monotone circuit complexity of functions in NP.  ...  / loglogn) bound. The simulation results are obtained using a new technique for dynamically averaging out a given work load among a set of processors operating in parallel.  ... 

Processor-Oblivious Parallel Stream Computations

Julien Bernard, Jean-Louis Roch, Daouda Traore
2008 16th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2008)  
We provide lower bounds for the parallel stream computation on p processors of different speeds with two models, a strict model and a buffered model; to our knowledge, these are new results.  ...  We study the problem of parallel stream computations on a multiprocessor architecture.  ...  Lower bounds for parallel stream computation We consider a machine with p processors of average speed Π with an input device and an output device.  ... 
doi:10.1109/pdp.2008.57 dblp:conf/pdp/BernardRT08 fatcat:zsaebfsvt5hcpivqbcgpknk4k4

Page 344 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
Barany (Louvain-la-Neuve) Immerman, Neil 84a:68041 Upper and lower bounds for first order expressibility. J. Comput. System Sci. 25 (1982), no. 1, 76-98.  ...  Other results obtained either are applicable to parallel compu- tations only or offer some new insight for sequential complexity theory.  ... 

GPU Implementation of the Branch and Bound Method for Knapsack Problems

Mohamed Esseghir Lalami, Didier El-Baz
2012 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum  
Branch and bound computations can be carried out either on the CPU or on a GPU according to the size of the branch and bound list.  ...  In this paper, we propose an efficient implementation of the branch and bound method for knapsack problems on a CPU-GPU system via CUDA.  ...  ACKNOWLEDGMENT Dr Didier El Baz would like to thank NVIDIA for his support through Academic Partnership.  ... 
doi:10.1109/ipdpsw.2012.219 dblp:conf/ipps/LalamiB12 fatcat:xdwu62ngmbafrhxq33yfq7i56a

Communication costs of Strassen's matrix multiplication

Grey Ballard, James Demmel, Olga Holtz, Oded Schwartz
2014 Communications of the ACM  
Matrix multiplication is one of the most fundamental problems in scientific computing and in parallel computing.  ...  Proving lower bounds on the communication of algorithms and finding algorithms that attain these bounds are therefore fundamental goals.  ...  In Section 2.2, we stated the communication cost of a new parallel algorithm for Strassen's matrix multiplication, matching the asymptotic lower bound.  ... 
doi:10.1145/2556647.2556660 fatcat:ifagecevkjdzjhkuomjnc6cfcu

Page 5892 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
This result implies a polynomial lower bound on PTIME-HARDWARE of parallel RAMs. All lower bounds obtained are substantially improved for the case that SPACE > n* for 0 < € < 1.  ...  For the complexity measure REVERSALS-SPACE-PARALLELISM (RSP), the lower bound 1(n!/3/ log, n) is established for the rec- ognition of a specific language on AM(k).  ... 

Page 7812 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
The transforma- tion of comparison model lower bounds, which are usually easier to obtain, to the parallel-random-access-machine, unifies some known lower bounds and gives new lower bounds for several  ...  Summary: “We provide general transformations of lower bounds in Valiant’s parallel-comparison-decision-tree model to lower bounds in the priority concurrent-read concurrent-write parallel- random-access-machine  ... 

Are search and decision programs computationally equivalent?

R M Karp, E Upfal, A Wigderson
1985 Proceedings of the seventeenth annual ACM symposium on Theory of computing - STOC '85  
From this point of view of sequential polynomial time computation, the answer to the question in the title is "yes".  ...  The technique used for the second lower bound is strong enough to establish the first tight time bounds for the PRIORITY model, which is the strongest parallel computation model.  ...  On the negative side, we prove lower bounds on any deterministic parallel reductions to the same oracles.  ... 
doi:10.1145/22145.22197 dblp:conf/stoc/KarpUW85a fatcat:bq54v7xcmfewnktvzcde7rqy24

Communication-optimal parallel algorithm for strassen's matrix multiplication

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz
2012 Proceedinbgs of the 24th ACM symposium on Parallelism in algorithms and architectures - SPAA '12  
Ballard, Demmel, Holtz, and Schwartz (SPAA'11) prove lower bounds on these communication costs, using expansion properties of the underlying computation graph.  ...  We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication.  ...  We made three observations from the lower bound results of [4] that lead to the new algorithm. First, the lower bounds for Strassen are lower than those for classical matrix multiplication.  ... 
doi:10.1145/2312005.2312044 dblp:conf/spaa/BallardDHLS12a fatcat:imvcz6bgsfho3px3hqgy4xs6jm

Communication-Optimal Parallel Algorithm for Strassen's Matrix Multiplication [article]

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz
2012 arXiv   pre-print
Ballard, Demmel, Holtz, and Schwartz (SPAA'11) prove lower bounds on these communication costs, using expansion properties of the underlying computation graph.  ...  We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication.  ...  We made three observations from the lower bound results of [4] that lead to the new algorithm. First, the lower bounds for Strassen are lower than those for classical matrix multiplication.  ... 
arXiv:1202.3173v1 fatcat:cmm4dxadg5hpvcxm2qqbe526qi
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