We consider the following communication problem: Each vertex of an undirected graph possesses a unique piece of information which must be sent to every other vertex in the graph. The mode of communication will be one-...
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We consider the following communication problem: Each vertex of an undirected graph possesses a unique piece of information which must be sent to every other vertex in the graph. The mode of communication will be one-way, point-to-point communication (i.e., one-way mail) in which one vertex may tell another everything it knows in a single transmission. We decribe nearly optimal parallel algorithms for disseminating the messages in certain prominent families of graphs (e.g., trees and hypercubes), and consider the complexity of the problem for general graphs.
Given n points in the plane the planar dominance counting problem is to determine for each point the number of points dominated by it. Point p is said to dominate point q if x(q)x(p) and y(q)y(p), when x(p) and y(p) a...
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Given n points in the plane the planar dominance counting problem is to determine for each point the number of points dominated by it. Point p is said to dominate point q if x(q)x(p) and y(q)y(p), when x(p) and y(p) are the x? and y-coordinate of p, respectively. We present two CREW PRAM parallel algorithms for the problem, one running in O(log n loglog n) time and and the other in O(lognloglogn/logloglogn) time both using O(n) processors. Some applicationsare also given.
We consider the problem of computing in parallel all pairs of shortest paths in a general large-scale directed network of N nodes. A hierarchical network decomposition algorithm is provided that yields for an importan...
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We consider the problem of computing in parallel all pairs of shortest paths in a general large-scale directed network of N nodes. A hierarchical network decomposition algorithm is provided that yields for an important subclass of problems log N savings in computation time over the traditional parallel implementation of Dijkstra's algorithm. Error bounds are provided for the procedure and are illustrated numerically for a problem motivated by intelligent transportation systems.
We examine parallel algorithms for molecular dynamics simulations involving long-range induction interactions. The algorithms are tested by performing molecular dynamics simulations of water with an intermolecular pot...
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We examine parallel algorithms for molecular dynamics simulations involving long-range induction interactions. The algorithms are tested by performing molecular dynamics simulations of water with an intermolecular potential that explicitly includes contributions from pair, three-body and induction interactions. Both cyclic and balanced force decomposition methods are implemented to decompose the parallelizable components of induction, pair and three-body interactions using a message passing interface. We report that more than 90% of the induction calculation, and 98% of the total calculation can be effectively parallelized. A reasonably good speedup of 15.7 times and an efficiency of 49.1% are obtained on 32 processors with the balance force decomposition algorithm. (C) 2007 Elsevier B.V. All rights reserved.
In this paper a parallel algorithm is given that, given a graph G = (V, E), decides whether G is a series parallel graph, and, if so, builds a decomposition tree for G of series and parallel composition rules. The alg...
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In this paper a parallel algorithm is given that, given a graph G = (V, E), decides whether G is a series parallel graph, and, if so, builds a decomposition tree for G of series and parallel composition rules. The algorithm uses O (log\E\log*\E\) time and O(\E\) operations on an EREW PRAM, and O (log \E\) time and O(\E\) operations on a CRCW PRAM. The results hold for undirected as well as for directed graphs. algorithms with the same resource bounds are described for the recognition of graphs of treewidth two, and for constructing tree decompositions of treewidth two. Hence efficient parallel algorithms can be found for a large number of graph problems on series parallel graphs and graphs with treewidth two. These include many well-known problems like all problems that can be stated in monadic second-order logic.
Finding common fixed points of a set of operators with some kind of contracting properties is a problem that has attracted much attention in the last decades. Probably the least demanding of such operators are the so-...
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Finding common fixed points of a set of operators with some kind of contracting properties is a problem that has attracted much attention in the last decades. Probably the least demanding of such operators are the so-called paracontractions, for which it is only needed that the image of a point under such operator is not farther away from the set of fixed points of the operator than the original point. In what follows, we present two parallel algorithms for finding common fixed points of a finite set of paracontractions;in the first one, the complete set of operators is involved at each iteration step;the second algorithm has a block-iterative nature.
The goal of this paper is to develop the parallel algorithms that, on input of a learning sample, identify a regular language by means of a nondeterministic finite automaton (NFA). A sample is a pair of finite sets co...
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The goal of this paper is to develop the parallel algorithms that, on input of a learning sample, identify a regular language by means of a nondeterministic finite automaton (NFA). A sample is a pair of finite sets containing positive and negative examples. Given a sample, a minimal NFA that represents the target regular language is sought. We define the task of finding an NFA, which accepts all positive examples and rejects all negative ones, as a constraint satisfaction problem, and then propose the parallel algorithms to solve the problem. The results of comprehensive computational experiments on the variety of inference tasks are reported. The question of minimizing an NFA consistent with a learning sample is computationally hard.
A parallel decompositional algorithm and VLSI architecture is proposed for computation of the output of a stack filter over a single window of input samples using Fibonacci p-codes. For a subclass of PBF's, a more...
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A parallel decompositional algorithm and VLSI architecture is proposed for computation of the output of a stack filter over a single window of input samples using Fibonacci p-codes. For a subclass of PBF's, a more efficient parallel algorithm and VLSI architecture for running stack filtering is also presented. The area-time complexities of the proposed designs are estimated.
The maximal linear forest problem is to find, given a graph G = (V, E), a maximal subset of V that induces a linear forest. Three parallel algorithms for this problem are presented. The first one is randomized and run...
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The maximal linear forest problem is to find, given a graph G = (V, E), a maximal subset of V that induces a linear forest. Three parallel algorithms for this problem are presented. The first one is randomized and runs in O(log n) expected time using n(2) processors on a CRCW PRAM. The second one is deterministic and runs in O(log(2) n) time using n(4) processors on an EREW PRAM. The last one is deterministic and runs in O(log(5) n) time using n(3) processors on an EREW PRAM. The results put the problem in the class NC.
We address a geometric problem called the segment dragging. We have n "obstacles" in the plane and want to preprocess them so that, given a query vertical line segment s, intersecting no obstacles, the first...
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We address a geometric problem called the segment dragging. We have n "obstacles" in the plane and want to preprocess them so that, given a query vertical line segment s, intersecting no obstacles, the first obstacle hit by s when we drag s horizontally to the right can be found efficiently. We present an O(log n) time, O(n) processor parallel algorithm for preprocessing when the obstacles are points or nonintersecting line segments. After preprocessing, a query can be answered in O(log n) time using a single processor. Our model of parallel computation is the EREW PRAM.
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