This paper presents very fast parallel algorithms for approximate edge coloring. Let log((1)) n = log n, log((k)) n = log(log((k-1)) n), and log*(n) = min{k \ log((k)) n /log(c/4) log*(n)])2 colors in O(log log*(n)) t...
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This paper presents very fast parallel algorithms for approximate edge coloring. Let log((1)) n = log n, log((k)) n = log(log((k-1)) n), and log*(n) = min{k \ log((k)) n < 1}. It is shown that a graph with n vertices and in edges can he edge colored with (2[log(1/4)log*(n)])(c) ([/log(c/4) log*(n)])2 colors in O(log log*(n)) time using O(m + n) processors on the EREW PRAM, where Delta is the maximum vertex degree of the graph and c is an arbitrarily large constant. It is also shown that the graph can he edge colored using at most [4 Delta (1+4/log log log*(Delta)) log(1/2) log*(Delta )1 colors in O(log Delta log log*(Delta)/log log log* (Delta) + log log*(n)) time using O(m + n) processors on the same model. O 2001 Elsevier Science B.V. All rights reserved.
The Drossel-Schwabl forest fire model is one of the best studied models of nonconservative self-organized criticality. However, using an alternative algorithm, which allows us to study the model on large statistical a...
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The Drossel-Schwabl forest fire model is one of the best studied models of nonconservative self-organized criticality. However, using an alternative algorithm, which allows us to study the model on large statistical and spatial scales, it has been shown to lack simple scaling. We thereby show that the considered model is not critical. This paper presents the algorithm and its parallel implementation in detail, together with large-scale numerical results for several observables. The algorithm can easily be adapted to related problems such as percolation.
Lyapunov and Stein matrix equations arise in many important analysis and synthesis applications in control theory. The traditional approach to solving these equations relies on the QR algorithm which is notoriously di...
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Lyapunov and Stein matrix equations arise in many important analysis and synthesis applications in control theory. The traditional approach to solving these equations relies on the QR algorithm which is notoriously difficult to parallelize. We investigate iterative solvers based on the matrix sign function and the squared Smith iteration which are highly efficient on parallel distributed computers. We also show that by coding using the parallel Linear Algebra Package (PLAPACK) it is possible to exploit the structure in the matrices and reduce the cost of these solvers. While the performance improvements due to the optimizations are modest, so is the coding effort. One of the optimizations, the updating of a QR factorization, has important applications elsewhere, e.g., in applications requiring the solution of a linear least-squares problem when the linear system is periodically updated. The experimental results on a Cray T3E attest to the high efficiency of these parallel solvers. (C) 2001 Academic Press.
The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorith...
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The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations. In some cases such algorithms will be much more complicated than a R-K methods, because it will require more function evaluation than well-known classical algorithms. However these evaluations can be accomplished fully parallel and the coefficients of truncated Taylor series can be calculated with matrix-vector operations. For large systems these operations suit for the parallel computers. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval and the local error of this solution at the interior points of the subinterval is less than that one at the end point. This property offers different facility for adaptive error control. This paper describes several above-mentioned algorithms and examines its consistency and stability properties. It demonstrates some numerical test results for stiff systems herewith we attempt to prove the efficiency of these new-old algorithms.
We consider the problem of computing the best swap edges of a shortest-path tree Tr rooted in r. That is, given a single link failure: if the path is not affected by the failed link, then the message will be delivered...
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Researchers have used nodes number to measure the extensibility of a topology. However, this metric is not very evident. In this paper, a specific metric called extensible density to measure the extensibilities of int...
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Researchers have used nodes number to measure the extensibility of a topology. However, this metric is not very evident. In this paper, a specific metric called extensible density to measure the extensibilities of interconnection networks is introduced. Some topologies have high degree of extensibilities, but efficient parallel algorithms can apply only on a special subclass of these topologies. Furthermore, the concept of density to measure the applicable extent of parallel algorithms have been extended.
This paper presents authors’ research on implementation of sorting nets in Field Programmable Logic Gates. As a theoretical base bitonic sorting nets were considered. During their research authors met several difficu...
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This paper presents authors’ research on implementation of sorting nets in Field Programmable Logic Gates. As a theoretical base bitonic sorting nets were considered. During their research authors met several difficulties which came from big digital resource requirements necessary to realize medium sizes sorting nets. A few techniques are proposed to obey these difficulties and advantages of sorting nets implementation in reprogrammable hardware are emphasized.
We present two multilevel parallel models based on MPI/MPI (MPI denoting Message Passing Interface) and MPI/OpenMP (OpenMP denoting Open Multi-Processing) for high-order CFD methods and compare their performances. The...
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We present parallel algorithms to find cut vertices, bridges, and Hamiltonian Path in bounded interval tolerance graphs. For a graph with n vertices, the algorithms require O (log n) time and use O (n) processors to r...
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ISBN:
(纸本)0769511538
We present parallel algorithms to find cut vertices, bridges, and Hamiltonian Path in bounded interval tolerance graphs. For a graph with n vertices, the algorithms require O (log n) time and use O (n) processors to run OR. Concurrent Read Exclusive Write parallel RAM (CREW PRAM) model of computation. Our approach transforms the original graph problem to a problem in computational geometry. The total work done by the parallel algorithms is comparable to the work done by the best known sequential algorithms for the more restricted class of graphs, namely, interval graphs and permutation graphs. In this sense our algorithms have optimal complementary.
In this paper, We proposed a new parallel algorithm for computing path expression, named parallel Cascade Semijoin (PCSJ). Moreover, a new scheduling strategy called right-deep zigzag tree is designed to further impro...
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ISBN:
(纸本)0769509967;0769509975
In this paper, We proposed a new parallel algorithm for computing path expression, named parallel Cascade Semijoin (PCSJ). Moreover, a new scheduling strategy called right-deep zigzag tree is designed to further improve the performance of the PCSJ algorithm. The experiments have been implemented in a NOW distributed and parallel environment. The results show that the PCSJ algorithm out-performs the other two parallel algorithms (the parallel version of forward pointer chasing algorithm (PFPC) and the index splitting parallel algorithm (IndexSplit)) when computing path expressions with restrictive predicates and that the right-deep zigzag tree scheduling strategy has the better performance that the right-deep tree scheduling strategy.
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