The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cl...
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The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set of paths is complete for the complexity class CC, the subset of P characterized by circuits composed of comparator gates. CC-completeness is believed to imply that, in the worst case, growing a cluster of size n requires polynomial time in n even on a parallel computer. A parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths, and then corrects defects in the guessed cluster through a nonlocal annihilation process. The parallel running time of the relaxation algorithm for two-dimensional internal DLA is studied by simulating it on a serial computer. The numerical results are compatible with a running time that is either polylogarithmic in n or a small power of ii. Thus the computational resources needed to grow large clusters are significantly less on average than the worst-case analysis would suggest. Fur a parallel machine with le processors, we show that random clusters in d dimensions can be generated in O((n/k + logic) n(2/d)) steps. This is a significant speedup over explicit sequential simulation, which takes O(n(1 + 2/d)) time on average. Finally, we show that in one dimension internal DLA can be predicted in O(log n) parallel time, and so is in the complexity class NC.
Distance hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. In this paper, we study properties of distance hereditary graphs from the v...
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Distance hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. In this paper, we study properties of distance hereditary graphs from the view point of parallel computations. We present efficient parallel algorithms for finding a minimum weighted connected dominating set, a minimum weighted Steiner tree, which take O(log n) time using O(n + m) processors on a CRCW PRAM, where n and m are the number of vertices and edges of a given graph, respectively. We also find a maximum weighted clique of a distance hereditary graph in O(log2 n) time using O(n + m) processors on a CREW PRAM.
The introduction of wide area measurements has brought a need for real time assessment methods of power systems, which are accurate and fast. The time varying coefficients in synchronous machine equations make it diff...
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The introduction of wide area measurements has brought a need for real time assessment methods of power systems, which are accurate and fast. The time varying coefficients in synchronous machine equations make it difficult to find solutions to obtain machine voltages, currents and flux linkages when expressed in phase quantities under transient conditions. The paper presents an approach to design power system transient stability assessment using direct methods for a multi-machine network based on multiple synchronized phasors, measured from Phasor Measurement Units (PMUs) and generator parameters. The generator rotor angle was derived from phasor measurements of voltage and current, and generator parameters using direct algorithm. The method assumes that a temporary fault is applied to the system therefore the pre-fault and post-fault conditions are similar. The multi-machine system was reduced to groups denoted Single Machine to Equivalent Bus (SMEB) models and another groups denoted Load Equivalent Bus (LEB) using parallel algorithms (PAs) [1]. The use of these PAs eliminates the SPMUs at each bus in the system, and it is required number of SPMUs only equals the number of generator buses. So that, the Equal Area Criterion in both rotor angle domain and time domain can be applicable for the SMEBs groups to assess the system stability in real-time through the Synchro-Phasors Measurements Units (SPMUs). A temporary three phase fault was simulated at test system comprises 2-machine, 8-bus network for validating the novel algorithm.
This paper presents a parallel algorithm for the following problem: given a simple graph G(V,E), color its edges with max{2(i-1) * ([Delta/2(i-1)] + 2), 2(i-1) * ([Delta/2(i-1)] + 3)} colors, 0 less than or equal to i...
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This paper presents a parallel algorithm for the following problem: given a simple graph G(V,E), color its edges with max{2(i-1) * ([Delta/2(i-1)] + 2), 2(i-1) * ([Delta/2(i-1)] + 3)} colors, 0 less than or equal to i less than or equal to [log Delta] - 1 such that al edges sharing a common vertex have different colors, where Delta ( = Delta(G)) is the maximum vertex degree, and \V\ = n, \E\ = m. This algorithm runs in 0((Delta/2(i-1))(3.5) log(3) Delta log n + (Delta/2(i-1))(3) log(4) n) time using 0(max{n(2), n(Delta/2(i-1))(3)}) processors. Particularly, it only requires 0(Delta(1.75) log(3) Delta log n + Delta(1.5) log(4) n) time and O(max{n(2), n Delta(1.5)}) processors when we use Delta + root Delta colors to color G's edges. If we use 2.5 Delta colors, it only requires O(log n log Delta) time and O(m) processors, based on a CREW PRAM. Unless otherwise specified, our computational model is a COMMON CRCW PRAM in which concurrent read and concurrent write are allowed. In addition, only writing the same value into a memory cell is successful when there exists write conflict.
We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for mult...
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We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets.
One of the most important aspect of molecular and computational biology is the reconstruction of evolutionary relationships. The area is well explored after decades of intensive research. Despite this fact there remai...
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One of the most important aspect of molecular and computational biology is the reconstruction of evolutionary relationships. The area is well explored after decades of intensive research. Despite this fact there remains a need for good and efficient algorithms that are capable of reconstructing the evolutionary relationship in reasonable time. Since the problem is computationally intractable, exact algorithms are used only for small groups of species. In the Maximum Parsimony approach the time of computation grows so fast when number of sequences increases, that in practice it is possible to find the optimal solution for instances containing about 20 sequences only. It is this reason that in practical applications, heuristic methods are used. In this paper, parallel adaptive memory programming algorithms based on Maximum Parsimony and some known neighborhood search methods for phylogenetic tree construction are proposed, and the results of computational experiments are presented. The proposed algorithms achieve a superlinear speedup and find solutions of good quality.
A multiprocessor machine, KUMARAN, with six target processors for real-time applications and an additional processor using the Unix operating system for development purposes has been implemented at San Diego State Uni...
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A multiprocessor machine, KUMARAN, with six target processors for real-time applications and an additional processor using the Unix operating system for development purposes has been implemented at San Diego State University. The machine is used to explore and evaluate parallel algorithms in the area of robot dynamics. A particular approximate algorithm for general inverse dynamics is considered here. The algorithm is based on the execution of each iteration of the recursive Newton-Euler formula associated with a manipulator link on a separate CPU, while the inter-processor synchronization is completely removed. Several experiments were run using a PUMA 560 manipulator as a specific example. Experiments have shown surprisingly small differences between the approximate and exact solutions.
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 fundamental problem of minimum computation has several well-studied generalizations such as prefix minima, range minima, and all nearest smaller values computations. Recent papers introduced parallel algorithms fo...
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The fundamental problem of minimum computation has several well-studied generalizations such as prefix minima, range minima, and all nearest smaller values computations. Recent papers introduced parallel algorithms for these problems when the n input elements are given from an integer domain [1..s], obtaining O(lglglgs) running time and linear work for s ≥ n. However, most of these algorithms have the running time of O(lglglgn) (rather than O(lglglgs)) for all values of s &le n, except for the case of s = O(1) in which case the running time is O(α(n)). In this paper we focus on the range s &le n and provide linear-work algorithms whose running time is O(lglglgs + f(n)) for all s ≥ 0, where f(n) is either one of the slow growing functions lg*n or α(n). We show how to generalize our algorithms to the case that the domain size s is unknown, with the same complexities. (All previous algorithms work only under the assumption that the domain size s is known.) Moreover, we make our algorithms output-sensitive with the lglglgs term replaced by lglglgM, where M is the maximum input value. In fact, for the minimum computation problem the running time is O(lglglgm) for all s ≥ 0, where m is the minimum input value.
The Boolean circuit has been an important model of parallel computation, but not many parallel algorithms have been designed on this model because it is 'awkward to program.' To overcome this drawback, we prop...
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The Boolean circuit has been an important model of parallel computation, but not many parallel algorithms have been designed on this model because it is 'awkward to program.' To overcome this drawback, we propose a description language for designing parallel algorithms on the Boolean circuit. This description language is to parallel algorithms what the pseudo-code is to sequential algorithms. Through example codes, we show that the description language is a convenient tool to design parallel algorithms due to its general iterative and recursive structures and the ease of modular design. (C) 2009 Elsevier B.V. All rights reserved.
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