In this paper we propose a parallel algorithm to construct a one-sided monotone polygon from a Hamiltonian 2-sep chordal graph which takes O(log n) time and uses O(n) processors on a CREW PRAM model. We also propose p...
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We present a technique for converting RNC algorithms into NC algorithms. Our approach is based on a parallel implementation of the method of conditional probabilities. This method was used to convert probabilistic pro...
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We present a technique for converting RNC algorithms into NC algorithms. Our approach is based on a parallel implementation of the method of conditional probabilities. This method was used to convert probabilistic proofs of existence of combinatorial structures into polynomial time deterministic algorithms. It has the apparent drawback of being extremely sequential in nature. We show certain general conditions under which it is possible to use this technique for devising deterministic parallel algorithms. We use our technique to devise an NC algorithm for the set balancing problem. This problem turns out to be a useful tool for parallel algorithms. Using our de-randomization method and the set balancing algorithm, we provide an NC algorithm for the lattice approximation problem. We also use the lattice approximation problem to bootstrap the set balancing algorithm, and the result is a more processor efficient algorithm. The set balancing algorithm also yields an NC algorithm for near-optimal edge coloring of simple graphs. Our methods also extend to the parallelization of various algorithms in computational geometry that rely upon the random sampling technique of Clarkson. Finally, our methods apply to constructing certain combinatorial structures, e.g., Ramsey graphs and independent sets and covers of hypergraphs. (C) 1994 Academic Press, Inc.
A number of parallel algorithms have been developed to solve large-scale real world problems. Although there has been much work on the design of parallel algorithms, there has been little on the design of Languages fo...
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A number of parallel algorithms have been developed to solve large-scale real world problems. Although there has been much work on the design of parallel algorithms, there has been little on the design of Languages for expressing these algorithms. This paper describes the BPL, a new parallel language designed for butterfly networks. The purpose of this language is to help designers in hiding the complexity of the algorithm and leaving details of mapping between data and processors for lower level. BPL provides a simpler virtual machine for the designer, in order to avoid thinking about control of processors and data. From another point of view, BPL helps designer to logically check the algorithm and correct ang. possible error in it. The paper gives some examples implemented by this language. In addition, we have also implemented a software toot which simulates the running of the algorithm on the network. The results lead us to believe that this language would be useful in representing all kinds of algorithms on this network including normal algorithms and others.
In this paper, we propose parallel algorithms for string matching problems on the recently proposed LARPBS model. Two subproblems are investigated. The exact string matching problem that consists in finding the occurr...
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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 alg...
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This paper considers the use of massively parallel architectures to execute a trace-driven simulation of a single cache set. A method is presented for the Least-Recently-Used (LRU) policy, which, regardless of the set...
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This paper considers the use of massively parallel architectures to execute a trace-driven simulation of a single cache set. A method is presented for the Least-Recently-Used (LRU) policy, which, regardless of the set size C, runs in time O(log N) using N processors on the exclusive read, exclusive write (EREW) parallel model. A simpler LRU simulation algorithm is given that runs in O(C log N) time using N/log N processors. We present timings of the second algorithm's implementation on the MasPar MP-1, a machine with 16 384 processors. A broad class of reference-based line replacement polices are considered, which includes LRU as well as the Least-Frequently-Used and Random replacement policies. A simulation method is presented for any such policy that on any trace of length N directed to a C line set runs in time O(C log N) time with high probability using N processors on the EREW model. The algorithms are simple, have very little space overhead, and are well suited for SIMD implementation.
Research in parallel algorithms for power system stability analysis started over a decade ago but has intensified recently. This experience with new parallel algorithms implemented on actual multiprocessors is startin...
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Research in parallel algorithms for power system stability analysis started over a decade ago but has intensified recently. This experience with new parallel algorithms implemented on actual multiprocessors is starting to highlight the constraints and some clear choices are beginning to emerge. In this paper, Gauss, Newton and relaxed Newton type algorithms are compared showing the last to be the most promising. Different implementation strategies are discussed together with their advantages and disadvantages. One of the algorithms, the Maclaurin-Newton, and much of the implementation techniques, especially the Toroidal method, are presented here for the first time and are shown to be improvements. However, the thrust of the paper is to show the superiority of the relaxed Newton methods and the importance of implementation techniques, the new methods being mere examples to demonstrate this.
We present a parallel algorithm that solves the single-source shortest path problem (SSSP) for a weighted digraph G = (V, E) in time O(log2n) using M(n) processors on an exclusive-read exclusive-write parallel random ...
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We present a parallel algorithm that solves the single-source shortest path problem (SSSP) for a weighted digraph G = (V, E) in time O(log2n) using M(n) processors on an exclusive-read exclusive-write parallel random access machine (EREW PRAM), where n = \V\, edge weights are drawn from the set {0, 1,..., k) for some constant k, and M(n) is the number of processors necessary to multiply two n x n integer matrices over a ring in O(log n) time (currently, M(n) = n2.376). This algorithm is a generalization of the O(log2n) time, M(n) Processor EREW PRAM algorithm due to Gazit and Miller for the SSSP problem in an unweighted digraph. We also briefly explain how our solution of the SSSP problem for a weighted digraph can be used to reduce the previous known processor bounds for a number of digraph problems to M(n) from THETA(n3) (within a polylog factor) without increasing the running time.
We develop efficient parallel algorithms for ther-dominating set and thep-center problems on trees. On a concurrent-read exclusive-write PRAM, our algorithm for ther-dominating set problem runs inO(logn log logn) time...
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We develop efficient parallel algorithms for ther-dominating set and thep-center problems on trees. On a concurrent-read exclusive-write PRAM, our algorithm for ther-dominating set problem runs inO(logn log logn) time withn processors. The algorithm for thep-center problem runs inO(log2 n log logn) time withn processors.
The compaction step of integrated circuit design motivates associating several kinds of graphs with a collection of non-overlapping rectangles in the plane. These graphs are intended to capture various visibility rela...
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The compaction step of integrated circuit design motivates associating several kinds of graphs with a collection of non-overlapping rectangles in the plane. These graphs are intended to capture various visibility relations amongst the rectangles in the collection. The contribution of this paper is to propose time- and cost-optimal algorithms to construct two such graphs, namely, the dominance graph (DG, for short) and the visibility graph (VG, for short). Specifically, we show that with a collection of n non-overlapping rectangles as input, both these structures can be constructed in theta(log n) time using n processors in the CREW model.
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