We present a randomized O(m log(2) n) work, O( polylogn) depth parallel algorithm for minimum cut. This algorithm matches thework bounds of a recent sequential algorithm by Gawrychowski, Mozes, andWeimann [ICALP'2...
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We present a randomized O(m log(2) n) work, O( polylogn) depth parallel algorithm for minimum cut. This algorithm matches thework bounds of a recent sequential algorithm by Gawrychowski, Mozes, andWeimann [ICALP'20], and improves on the previously best parallel algorithm by Geissmann and Gianinazzi [SPAA'18], which performs O(m log(4) n) work in O(polylogn) depth. Our algorithm makes use of three components that might be of independent interest. First, we design a parallel data structure that efficiently supports batched mixed queries and updates on trees. It generalizes and improves thework bounds of a previous data structure of Geissmann and Gianinazzi and iswork efficient with respect to the best sequential algorithm. Second, we design a parallel algorithm for approximate minimum cut that improves on previous results by Karger and Motwani. We use this algorithm to give a work-efficient procedure to produce a tree packing, as in Karger's sequential algorithm for minimum cuts. Last, we design an efficient parallel algorithm for solving the minimum 2-respecting cut problem.
One of the important problems in the use of remote sensing from satellites is three-dimensional modeling of surface—fragments both dynamic (e.g., ocean surface) and slowly varying ones. Some researchers propose the u...
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Enormous river basin information has been collected by for high resolution of the physically-based distributed hydrological model, while the scales of computational domain are often restricted by the intensive calcula...
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Direct multisearch (DMS) is a derivative-free optimization class of algorithms, suited for computing approximations to the complete Pareto front of a given multiobjective optimization problem. In DMS class, constraint...
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Direct multisearch (DMS) is a derivative-free optimization class of algorithms, suited for computing approximations to the complete Pareto front of a given multiobjective optimization problem. In DMS class, constraints are addressed with an extreme barrier approach, only evaluating feasible points. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with the definition of a search step based on the minimization of quadratic polynomial models, corresponding to the algorithm BoostDMS. In this work, we propose and numerically evaluate strategies to improve the performance of BoostDMS, mainly through parallelization applied to the search and to the poll steps. The final parallelized version not only considerably decreases the computational time required for solving a multiobjective optimization problem, but also increases the quality of the computed approximation to the Pareto front. Extensive numerical results will be reported in an academic test set and in a chemical engineering application.
Based on two-grid discretizations, some local and parallel stabilized finite element methods are proposed and investigated for the Stokes problem in this paper. For the finite element discretization, the lowest equal-...
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Based on two-grid discretizations, some local and parallel stabilized finite element methods are proposed and investigated for the Stokes problem in this paper. For the finite element discretization, the lowest equal-order finite element pairs are chosen to circumvent the discrete inf-sup condition. In these algorithms, we derive the low-frequency components of the solution for the Stokes problem on a coarse grid and catch the high-frequency components on a fine grid using some local and parallel procedures. Optimal error bounds are demonstrated and some numerical experiments are carried out to support theoretical results.
The 3D surface reconstruction is critical for various applications, demanding efficient computational approaches. Traditional Radial Basis Functions (RBFs) methods are limited by increasing data points, leading to slo...
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ISBN:
(纸本)9798350363074;9798350363081
The 3D surface reconstruction is critical for various applications, demanding efficient computational approaches. Traditional Radial Basis Functions (RBFs) methods are limited by increasing data points, leading to slower execution times. Addressing this, our study introduces an experimental parallelization effort using Julia, as well-known for high-performance scientific computing. We developed an initial sequential RBF algorithm in Julia, then expanded it to a parallel model, exploiting Multi-Threading to enhance execution speed while maintaining accuracy. This initial exploration into Julia's parallel computing capabilities shows marked performance gains in 3D surface reconstruction, offering promising directions for future research. Our findings affirm Julia's potential in computationally intensive tasks, with test results confirming the expected time efficiency improvements.
For parallel-in-time simulation of large-scale power systems, this paper proposes a differential transformation based adaptive Parareal method for significantly improved convergence and time performance compared to a ...
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For parallel-in-time simulation of large-scale power systems, this paper proposes a differential transformation based adaptive Parareal method for significantly improved convergence and time performance compared to a traditional Parareal method, which iterates a sequential, numerical coarse solution over extended time steps to connect parallel fine solutions within respective time steps. The new method employs the differential transformation to derive a semi-analytical coarse solution of power system differential-algebraic equations, by which the order and time step, as well as the window length with a multi-window solution strategy, can adaptively vary with the response of the system. Thus, the new method can reduce divergences and also speed up the overall simulation. Extensive tests on the IEEE 39-bus system and the Polish 2383-bus system have verified the performance of the proposed method.
The high intensity of research and modeling in fields of mathematics, physics, biology and chemistry requires new computing resources. For the big computational complexity of such tasks computing time is large and cos...
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The high intensity of research and modeling in fields of mathematics, physics, biology and chemistry requires new computing resources. For the big computational complexity of such tasks computing time is large and costly. The most efficient way to increase efficiency is to adopt parallel principles. Purpose of this paper is to present the issue of parallel computing with emphasis on the analysis of parallel systems, the impact of communication delays on their efficiency and on overall execution time. Paper focuses is on finite algorithms for solving systems of linear equations, namely the matrix manipulation (Gauss elimination method, GEM). algorithms are designed for architectures with shared memory (open multiprocessing, openMP), distributed-memory (message passing interface, MPI) and for their combination (MPI + openMP). The properties of the algorithms were analytically determined and they were experimentally verified. The conclusions are drawn for theory and practice.
In this paper, we present an efficient parallel derandomization method for randomized algorithms that rely on concentrations such as the Chernoff bound. This settles a classic problem in parallel derandomization, whic...
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ISBN:
(纸本)9798400703836
In this paper, we present an efficient parallel derandomization method for randomized algorithms that rely on concentrations such as the Chernoff bound. This settles a classic problem in parallel derandomization, which dates back to the 1980s. Concretely, consider the set balancing problem where m sets of size at most B are given in a ground set of size n, and we should partition the ground set into two parts such that each set is split evenly up to a small additive (discrepancy) bound. A random partition achieves a discrepancy of O (root s log m) in each set, by Chernoff bound. We give a deterministic parallel algorithm that matches this bound, using near-linear work (O) over tilde (m + n + Sigma(m)(i=1) vertical bar S-i vertical bar and polylogarithmic depth poly(log (mn)). The previous results were weaker in discrepancy and/or work bounds: Motwani, Naor, and Naor [FOCS'89] and Berger and Rompel [FOCS'89] achieve discrepancy BY center dot $ (p B log <) with work <(O)over tilde> (m + n + Sigma(m)(i=1) vertical bar S-i vertical bar)center dot m(Theta(1/epsilon)) and polylogarithmic depth;the discrepancy was optimized to O (root s log m) in later work, e.g. by Harris [Algorithmica'19], but the work bound remained prohibitively high at (O) over tilde (m(4)n(3)). Notice that these would require a large polynomial number of processors to even match the near-linear runtime of the sequential algorithm. Ghaffari, Grunau, and Rozhon [FOCS'23] achieve discrepancy s/poly(log(nm)) + O(root s log m) with near-linear work and polylogarithmic-depth. Notice that this discrepancy is nearly quadratically larger than the desired bound and barely sublinear with respect to the trivial bound of s. Our method is different from prior work. It can be viewed as a novel bootstrapping mechanism that uses crude partitioning algorithms as a subroutine and sharpens their discrepancy to the optimal bound. In particular, we solve the problem recursively, by using the crude partition in each iterat
The digital age came with an extraordinary ability to generate data across organizations, people, and devices, data that needs to be analyzed, processed and stored. A well-known technique for analyzing this kind of da...
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