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Intersecting line segments in parallel with an output-sensitive number of processors 89

Intersecting line segments in parallel with an output-sensit...

引用

1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Goodrich, Michael T. Department of Computer Science Johns Hopkins University BaltimoreMD21218 United States

ISBN: (纸本)089791323X

We give an efficient parallel algorithm for constructing the arrangement of n line segments in the plane, i.e., the planar graph 'determined by the segment endpoints and intersections. Our algorithm is efficient relative to three efficiency measures it is an NC algorithm, it has a small time-processor product, and it is output-size sensitive. In particular, it runs in O(log 2 n) time using O(n + k/log n) processors in the CREW PRAM model, where k is the size of the output (which is Ω(n 2) in the worst case). The algorithm does not receive the value of k as input, it determines it on-line. © 1989 acm.

关键词： parallel algorithms

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The power of parallel pointer manipulation 89

The power of parallel pointer manipulation

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Lam, Tak Wah Ruzzo, Walter L. Department of Computer Science University of Hong Kong Pokfulam Road Hong Kong Computer Science Department University of Washington SeattleWA98195 United States

ISBN: (纸本)089791323X

An HMM is a very simple parallel machine consisting of finite state devices that can manipulate pointers to each other. The more commonly studied PRAM is a much richer parallel machine with a shared global memory and arithmetic capabilities. We define a natural restriction of the PRAM that is shown to be equivalent to the HMM to within a constant factor in both time and hardware simultaneously. Basically, the restricted PRAM is a Concurrent Read, Owner Write (CROW) PRAM, stripped of arithmetic capabilities, except for successor (+1) a doubling ( x 2) operations. © 1989 acm.

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An efficient parallel algorithm for computing a large independent set in planar graph 89

An efficient parallel algorithm for computing a large indepe...

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Chrobek, Maxek Naor, Joseph Department of Mathematics and Computer Science University of California RiversideCA92521 United States Department of Computer Science Stanford University StanfordCA94305-2140 United States

ISBN: (纸本)089791323X

Let (G) denote the independence number of a graph G, that is the maximum number of pairwise independent vertices in G. We present a parallel algorithm that computes in a planar graph G = (V, E), an independent set I ⊂ V such that III > α(G)/2. The algorithm runs in time O(log 2 n) and requires a linear number of processors. This is achieved by defining a set. of reductions that can be executed "locally" and simultaneously;further more, it is shown that a constant fraction of the vertices in the graph are reducible. This is the best known approximation scheme when the number of processors available is linear;parallel implementation of known sequential algorithms requires many more processors. © 1989 acm.

关键词： parallel algorithms

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parallel RAMs with bounded memory wordsize 89

Parallel RAMs with bounded memory wordsize

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Bellantoni, Stephen J. Department of Computer Science University of Toronto Canada

ISBN: (纸本)089791323X

The PRAM model of parallel computation is examined with respect to wordsize, the number of bits which can be held in each global memory cell. First, adversary arguments are used to show the incomparability of certain machines which store the same amount of global information but which differ in wordsize. Next, for machines with infinitely many memory cells, a counting argument is used to show a large lower bound and to separate a hierarchy of machine classes based on wordsize. Finally, an efficient simulation by boolean circuits is used to give a simple new proof of the tight ω(log n / log log n ) time bound for PARITY on small-word size machines. Overall the results suggest that, in some circumstances, the memory word size is a more significant resource than the write resolution rule, number of memory cells, or number of processors. © 1989 acm.

关键词： Random access storage

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Conflict-free access of arrays in a parallel processor 89

Conflict-free access of arrays in a parallel processor

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Lee, D.-L. Wang, Y.H. Department of Computer Science York University North YorkONM3J1P3 Canada

ISBN: (纸本)089791323X

Let T be a collection of data templates of an N × N matrix, T = {row, column, forward diagonal, backward diagonal}. In the context of parallel processing, the question of whether it is possible or not for a parallel processor with N processing elements, N memory modules, and an interconnection network to allow parallel, conflict-free access to any instance of any data templates in T for N = 2n and any n > 1 has been open for a long time. The problem essentially concerns whether there exists any valid skewing scheme that can be realized in terms of interconnection networks. In this paper we will answer this open question by presenting a valid skewing scheme and a simple interconnection network that efficiently implements the skewing scheme in question. © 1989 acm.

关键词： Interconnection networks (circuit switching)

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On the parallel complexity of integer programming 89

On the parallel complexity of integer programming

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Deng, Xiaotie Dept. of Operations Research Stanford University United States Dept. of Computer Science and Engineering UC at San Diego United States

ISBN: (纸本)089791323X

We show that the several problems, whose complexity with respect P and NC was open, are equivalent under NC-reductions. These include: (1) Finding the optimal solution of a two-variable integer program;(2) Determining whether a set of linear inequalities in two dimensions has all integer solution;(3) Finding all intermediate results in the Euclidean algorithm for the greatest common divisor of two integers;(4) Finding integers x and y that minimize mx+ny > 0 (as is well known, the result mx+ny is the greatest common divisor of m and n). We also show that integer programming can be NC-reduced to the basis reduction problem (and tiffs holds in any fixed dimension). Thus, basis reduction is the only step in Lenstra's algorithm that is not easily parallelizable. © 1989 acm.

关键词： Integer programming

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On parallel evaluation of game trees 89

On parallel evaluation of game trees

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Karp, Richard M. Zhang, Yanjun Computer Science Division University of California BerkeleyCA94720 United States

ISBN: (纸本)089791323X

We present parallel algorithms for evaluating game trees. These algorithms parallelize the "left-To-right" sequential algorithm for evaluating AND]OR trees and the α-β pruning procedure for evaluating MIN/MAX trees. We show that, on every instance of a uniform tree, these parallel algorithms achieve a linear speed-up over their corresponding sequential algorithms, if the number of processors used is close to the height of the input tree. These are the first non-Trivial deterministic speed-up bounds known for the "left-To-right" algorithm and the α-β pruning procedure. © 1989 acm.

关键词： parallel algorithms

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Optimal VLSI architectures for multidimensional DFT 89

Optimal VLSI architectures for multidimensional DFT

引用

1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Bilardi, Gianfranco Hornick, Scot W. Sarrafzadeh, Majid Department of Computer Science Cornell University Upson Hall IthacaNY14853 United States Andersen Consulting Center for Strategic Tech. Res. 100 S. Wacker ChicagoIL60606 United States Dept. of Elec. Eng. and Comp. Sci. Technological Institute Northwestern University EvanstonIL60208 United States

ISBN: (纸本)089791323X

A family of VLSI architectures for computing an (n 1 × n 2 × • • " × nd)-point multidimensional D1VF (MDDFT) over Zm, the ring of integers modulo M, is presented. These architectures achieve VLSI area A = 0 ((NZlog2M)/T 2) for any comptitation time T ϵ [ω(logN),O (ωNlogM)], where N = I'Int and it is k=l assumed that logM = O(logN). A lower bound argument is developed to show that the proposed architectures are area-Time optimal. The appficability of these architectures to computation of the MDDFT over the complex field is also discussed. Using fixed-point arithmetic with b bits of precision, their area-Time performance is AT2= O(N2b 2) for any computation time T ϵ [ω(logN),O(√Nb)]. © 1989 acm.

关键词： Fixed point arithmetic

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Locating faults in a constant number of parallel testing rounds 89

Locating faults in a constant number of parallel testing rou...

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Beigel, Richard Kosaraju, S. Rao Sullivan, Gregory F. Dept. of Computer Science Johns Hopkins University BaltimoreMD21218 United States

ISBN: (纸本)089791323X

Consider a system of processing elements in which elements may administer tests to other elements. We show, surprisingly, that a constant, number of rounds of parallel testing are sufficient to identify all faults (in all cases where fault identification is possible). We also present an O(loglogn/t t) algorithm with a small constant of proportionality, where n denotes the total number of processors and t denotes the number of faulty processors. Both of these results improve upon the previous best, which was O(log n/t t) rounds. For the problems of identifying a single faulty processor (diagnosis-with-repair) and identifying a single good processor, we present an oblivious constant-Time algorithm using a fixed 3-regular interconnect that tolerates a linear number of faults. This contrasts with the well-known result that every oblivious algorithm for complete diagnosis must use a number of rounds that is linear in t. © 1989 acm.

关键词： parallel algorithms

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Constructing trees in parallel 89

Constructing trees in parallel

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Atallah, M.J. Kosaraju, S.R. Larmore, L.L. Miller, G.L. Teng, S.-H. Department of Computer Science Purdue University United States Department of Computer Science Johns Hopkins University United States ICS UC Irvine United States School of Computer Science CMU United States Department of Computer Science USC United States

ISBN: (纸本)089791323X

An O(log 2 n) time, n2/logn processor as well as an O(log n) time, n3/log n processor CREW deterministic parallel algorithms are presented for constructing Huffman codes from a given list of frequences. The time can be reduced to O(log n(loglog n) 2) on an CRCW model, using only n2/(log log n) 2 processors. Also presented is an optimal O(log n) time, O(n/log n) processor EREW parallel algorithm for constructing a tree given a list of leaf depths when the depths are monotonic. An O(log 2 n) time, n processor parallel algorithm is given for the general tree construction problem. We also give an O(log 2 n) time n2/log2n processor algorithm which finds a nearly optimal binary search tree. An O(log 2 n) time n 2 36 processor algorithm for recognizing linear context free languages is given. A crucial ingredient in achieving those bounds is a formulation of these problems as multiplications of special matrices which we call concave matrices. The structure of these matrices makes their parallel multiplication dramatically more efficient than that of arbitrary matrices. © 1989 acm.

关键词： parallel algorithms

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