Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperati...
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The article explores the possibility of computing parallel data compression using cubic spline. For example, ways to parallel the process of digital processing of seismic signals have been considered. The main perform...
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ISBN:
(数字)9781728173863
ISBN:
(纸本)9781728173870
The article explores the possibility of computing parallel data compression using cubic spline. For example, ways to parallel the process of digital processing of seismic signals have been considered. The main performance indicators of parallel algorithms have been compared with consecutive algorithms. Spline methods are a versatile signal processing tool. It is more accurate than other mathematical methods, information equality is faster, and maintenance costs are much lower. On the other hand, the equipment used in such systems must also meet high performance requirements. To achieve high speeds, parallel algorithms were developed using OpenMP and MPI technologies and implemented in the architecture of multi-core processors. A mathematical method for the parallel calculation of the coefficients of a cubic spline has been developed and a parallel signal processing algorithm has been developed on its basis. As an example, parallelization is a computation during seismic signal processing. The main indicators of efficiency and acceleration of the parallel algorithm were compared with the sequential algorithm. Explained the relevance of the use of parallel numerical systems, described the main approaches to the distribution of processes and methods of data processing, described the principles of parallel programming technology, studied the basic parameters of parallel algorithms for the initial calculation of the numerical value of cubic spline. The parallel algorithm considered for constructing the cubic spline of defect 1 as p - > n leads to the construction of a local cubic spline on each grid interval ω.
Frequent itemset mining is the most important step of association rule mining. Due to the large size of datasets, many parallel mining methods have been introduced to divide datasets or to distribute mining processes,...
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Most studies related to parallel and portfolio search for solving combinatorial problems, such as those found in Boolean satisfiability or constraint programming, evaluate search cost in terms of runtime. However, giv...
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Most studies related to parallel and portfolio search for solving combinatorial problems, such as those found in Boolean satisfiability or constraint programming, evaluate search cost in terms of runtime. However, given the complex computing architectures available today and the focus on the environmental impact of computing, there is growing interest in also considering the energy cost associated with solving these problems. In the context of combinatorial problem-solving, a simple approximation of energy cost is the product of the number of machines multiplied by the runtime spent to solve a problem instance. However, the picture is much more complex due to the impact that the distribution of runtimes, even for solving a single specific instance, can have on search cost. In this paper we present an initial, but comprehensive, study on the impact of runtime distribution on the amount of energy required for combinatorial problem solving characterised by two common continuous runtime distributions, namely the Weibull and Pareto distributions. The primary contribution of this paper is to demonstrate that there is an interesting and non-trivial relationship between runtime, parallelisation, and energy cost in combinatorial solving that is worthy of further study. (C) 2019 Elsevier B.V. All rights reserved.
The Sequential Ordering Problem (SOP) is a combinatorial optimization problem. Given a directed weighted graph and an unweighted directed graph representing precedence constraints among vertices, find a minimum-cost H...
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The Sequential Ordering Problem (SOP) is a combinatorial optimization problem. Given a directed weighted graph and an unweighted directed graph representing precedence constraints among vertices, find a minimum-cost Hamiltonian path that satisfies the precedence constraints. Previous work on this problem included heuristic solutions and sequential optimal algorithms. To the best of our knowledge, there is no parallel optimal algorithm for the SOP. In this work, we propose a parallel optimal algorithm for the SOP using a branch-and-bound approach. Our current experimental results using 116 standard benchmark instances show that with a 2-hour time limit, the proposed parallel algorithm can solve 75 instances compared to 66 instances solved by the existing sequential algorithm. The average speedup across all solved instances is 2.05 for 4 threads. The best speedup with 4 threads is over 21.
We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a ...
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We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a regular grid of cells, each cell being affected to a single processor. Each processor operates on local data, starting from its cell location and extending its search to the neighborhood cells in a spiral search way. In order to deal with large-size problems, memory size and processor number are fixed as O(N), where N is the problem size. Then one key point is that closest point searching in the plane is performed in O(1) expected time for uniform or bounded distribution, for each processor independently. We define a generic loop that models the parallel projection between graphs and their matching, as executed by the many cells at a given level of computation granularity. To illustrate its efficacy and versatility, we apply the CMM, on GPU platforms, to two problems in image processing: superpixel segmentation and stereo matching energy minimization. Firstly, we propose an extended version of the well-known SLIC superpixel segmentation algorithm, which we call SPASM algorithm, by using a parallel 2D self organizing map instead of k-means algorithm. Secondly, we investigate the idea of distributed variable neighborhood search, and propose a parallel search heuristic, called distributed local search (DLS), for global energy minimization of stereo matching problem. We evaluate the approach with regards to the state-of-the-art graph cut and belief propagation algorithms. For each problem, we argue that the parallel GPU implementation provides new competitive quality/time trade-offs, with substantial acceleration factors as the problem size increases. (C) 2017 Elsevier B.V. All rights reserved.
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense...
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We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically Theta((n/p)(2/3)) p-parallel queries for element distinctness and Theta((n/p)(k/(k+ 1))) for k-sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p-parallel query complexity are polynomially related for all total functions f when p is small compared to f's block sensitivity.
For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, the parallel matrix sweep algorithm, conjugate gradient method with preconditioner, and square root m...
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For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, the parallel matrix sweep algorithm, conjugate gradient method with preconditioner, and square root method are proposed and implemented numerically on multi-core CPU Intel with graphics processors NVIDIA. Investigation of efficiency and optimization of parallel algorithms for solving the problem with quasi-model data are performed. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.
A cut tree is a combinatorial structure that represents the edge-connectivity between all pairs of vertices of an undirected graph. Cut trees solve the all pairs minimum s-t-cut problem efficiently. Cut trees have a l...
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A cut tree is a combinatorial structure that represents the edge-connectivity between all pairs of vertices of an undirected graph. Cut trees solve the all pairs minimum s-t-cut problem efficiently. Cut trees have a large number of applications including the solution of important combinatorial problems in fields such as graph clustering and graph connectivity. They have also been applied to scheduling problems, social network analysis, biological data analysis, among others. Two sequential algorithms to compute a cut tree of a capacitated undirected graph are well known: the Gomory-Hu algorithm and the Gusfield algorithm. In this work three parallel cut tree algorithms are presented, including parallel versions of Gusfield and Gomory Hu algorithms. A hybrid algorithm that combines techniques from both algorithms is proposed which provides a more robust performance for arbitrary instances. Experimental results show that the three algorithms achieve significant speedups on real and synthetic graphs. We discuss the trade-offs between the alternatives, each of which presents better results given the characteristics of the input graph. On several instances the hybrid algorithm outperformed both other algorithms, being faster than the parallel Gomory Hu algorithm on most instances. (C) 2017 Elsevier Inc. All rights reserved.
We describe a new Monte Carlo method based on a multilevel method for computing the action of the resolvent matrix over a vector. The method is based on the numerical evaluation of the Laplace transform of the matrix ...
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We describe a new Monte Carlo method based on a multilevel method for computing the action of the resolvent matrix over a vector. The method is based on the numerical evaluation of the Laplace transform of the matrix exponential, which is computed efficiently using a multilevel Monte Carlo method. Essentially, it requires generating suitable random paths which evolve through the indices of the matrix according to the probability law of a continuous-time Markov chain governed by the associated Laplacian matrix. The convergence of the proposed multilevel method has been discussed, and several numerical examples were run to test the performance of the algorithm. These examples concern the computation of some metrics of interest in the analysis of complex networks, and the numerical solution of a boundary-value problem for an elliptic partial differential equation. In addition, the algorithm was conveniently parallelized, and the scalability analyzed and compared with the results of other existing Monte Carlo method for solving linear algebra systems.
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