A basic problem in graphs and hypergraphs is that of finding a large independent set-one of guaranteed size. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a funda...
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A basic problem in graphs and hypergraphs is that of finding a large independent set-one of guaranteed size. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza [J. Graph Theory, 15 (1991), pp. 99-107] have shown a certain lower bound alpha(k)(H) on the size of a maximum independent set in a given k-uniform hypergraph H and have also presented an efficient sequential algorithm to find an independent set of size alpha k(H). They also show that alpha(k)(H) is the size of the maximum independent set for various hypergraph families. Here, we show that an RNC algorithm due to Beame and Luby [in Proceedings of the ACM-SIAM Symposium on Discrete algorithms, 1990, pp. 212-218] finds an independent set of expected size alpha(k)(H) and also derandomizes it for certain special cases. (An intriguing conjecture of Beame and Luby implies that understanding this algorithm better may yield an RNC algorithm to find a maximal independent set in hypergraphs, which is among the outstanding open questions in parallel computation.) We also present lower bounds on independent set size for nonuniform hypergraphs using this algorithm. For graphs, we get an NC algorithm to find independent sets of size essentially that guaranteed by the general (degree-sequence based) version of Turan's theorem.
Understanding the demixing effect on the dispersion of particles by large-scale turbulence is very important in practical applications. Using pseudospectral and Lagrangian approaches, we have simulated a three-dimensi...
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Understanding the demixing effect on the dispersion of particles by large-scale turbulence is very important in practical applications. Using pseudospectral and Lagrangian approaches, we have simulated a three-dimensional particle-laden mixing layer under one-way coupling effect. However, the computer resource required to simulate such a two-phase flow with high Reynolds number and two-way momentum coupling effect exceeds the limit of the current single processor. In this paper. the computation of particles and the two-way momentum coupling terms are partitioned in the span-wise direction because particles are distributed most evenly in this direction. The computation of the tree-dimensional flow field is first partitioned into three groups of processors because of the most independence of the computation among the three spatial dimensions. In each group, the domain is then partitioned using two different schemes based on the property of the fast Fourier transformation. The first one, the master slave scheme, is employed for Algorithm MS due to its simplicity and overlapping of communication and computation. The second one, the transpose approach, is used for Algorithm TP order to partition all of the flow field computation. An analysis shows that compared to Algorithm MS, Algorithm TP can also reduce nearly a half of the amount of communication work. Experiments show that Algorithm MS has obtained a speedup of 4.3 using 9 HP workstations and a speedup of 6.4 using 15 nodes of IBM SP-2 for a problem size on the order of 64(3), and Algorithm TP has achieved speedups 44% higher than Algorithm MS. (C) 2001 Elsevier Science.
Rapid advancements in adaptive sonar beamforming algorithms have greatly increased the computation and communication demands on beamforming arrays, particularly for applications that require in-array autonomous operat...
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Rapid advancements in adaptive sonar beamforming algorithms have greatly increased the computation and communication demands on beamforming arrays, particularly for applications that require in-array autonomous operation. By coupling each transducer node in a distributed array with a microprocessor, and networking them together, embedded parallel processing for adaptive beamformers can significantly reduce execution time, power consumption and cost, and increase scalability and dependability. In this paper, the basic narrowband Minimum Variance Distortionless Response (MVDR) beamformer is enhanced by incorporating broadband processing, a technique to enhance the robustness of the algorithm, and speedup of the matrix inversion task using sequential regression. Using this Robust Broadband MVDR (RB-MVDR) algorithm as a sequential baseline, two novel parallel algorithms are developed and analyzed. Performance results are included, among them execution time, scaled speedup, parallel efficiency, result latency and memory utilization. The testbed used is a distributed system comprised of a cluster of personal computers connected by a conventional network.
The Bean critical-state model describes the Penetration of magnetic field into type-II superconductors. Mathematically, it is a free boundary problem, and fast algorithms for its solution are needed in applied superco...
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The Bean critical-state model describes the Penetration of magnetic field into type-II superconductors. Mathematically, it is a free boundary problem, and fast algorithms for its solution are needed in applied superconductivity. Existence and uniqueness of solution, parallel algorithms, stability, and error estimation for this model are discussed.
In this paper, we will be mainly concerned with a parallel algorithm (in time and space) which is used to solve the incompressible Navier-Stokes problem. This relies on two main ideas: (a) a splitting of the main diff...
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In this paper, we will be mainly concerned with a parallel algorithm (in time and space) which is used to solve the incompressible Navier-Stokes problem. This relies on two main ideas: (a) a splitting of the main differential operator which permits to consider independently the most important difficulties (nonlinearity and incompressibility) and (b) the approximation of the resulting stationary problems by a family of second-order one-dimensional linear systems. The same strategy can be applied to two-dimensional and three-dimensional problems and involves the same level of difficulty. It can be also useful for the solution of other more complicate systems like Boussinesq or turbulence models. The behavior of the method is illustrated with some numerical experiments.
This paper proposes different strategies of parallelizing a multi-criteria GRASP (Greedy Randomized Adaptive Search Problem) algorithm. The parallel GRASP algorithm is applied to the multi-criteria minimum spanning tr...
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This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error est...
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This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria for these methods. In the case of asynchronous iterations, macro-iterations are used as a tool in order to obtain estimates.
In this paper, we present a constant time algorithm for solving three dimensional block-based medial axis transform (3D BB-MAT, for short) on the array with reconfigurable optical buses (AROB). The main contribution o...
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The construction of the concept lattice of a context is a time consuming process. However, in many practical cases where FCA has proven to provide theoretical strength, e.g., in data mining, the volume of data to anal...
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Determining the three-dimensional structure of proteins is crucial to efficient drug design and understanding biological processes. One successful method for computing the molecule's shape relies on inter-atomic d...
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Determining the three-dimensional structure of proteins is crucial to efficient drug design and understanding biological processes. One successful method for computing the molecule's shape relies on inter-atomic distance bounds provided by Nuclear Magnetic Resonance spectroscopy. The accuracy of computed structures as well as the time required to obtain them are greatly improved if the gaps between the upper and lower distance-bounds are reduced. These gaps are reduced most effectively by applying the tetrangle inequality, derived from the Cayley-Menger determinant, to all atom-quadruples. However, tetrangle-inequality bound-smoothing is an extremely computation intensive task, requiring O(n(4)) time for an n-atom molecule. To reduce computation time, we propose a novel coarse-grained parallel algorithm intended for a Beowulf-type cluster of PCs. The algorithm employs p <= n/6 processors and requires O(n(4)/p) time and O(p(2)) communications, where n is the number of atoms in a molecule. The number of communications is at least an order of magnitude lower than in the earlier parallelizations. Our implementation utilized processors with at least 59% efficiency (including the communication overhead)-an impressive figure for a non-embarrassingly parallel problem on a cluster of workstations.
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