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Efficient parallel shortest-paths in digraphs with a separator decomposition 93

Efficient parallel shortest-paths in digraphs with a separat...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Cohen, Edith AT and T Bell Laboratories Murray HillNJ07974 United States

ISBN: (纸本)0897915992

We consider shortest paths and reachability problems on directed graphs with real-valued edge weights. For sparser graphs, the known AfC algorithms for these problems perform much more work than their sequential counterparts. In this paper we present efficient parallel algorithms for families of graphs, where a separator decomposition is either provided with the input or is easily obtainable. (A separator is a subset of the vertices that its removal splits the graph into connected components, where the number of vertices in each component is at most a fixed fraction of the size of the graph. A separator decomposition is a recursive decomposition of the graph using separators.) Let G = (V, E), where n = |V|, be a weighted directed graph with a fc"-separator decomposition (where subgraphs with k vertices have separators of size 0(k)). We present an MC algorithm that computes shortest paths from s sources to all other vertices using 0{n3,i + s(n + n21)) work. Reachability from s sources can be computed using 0(M(n'') log2 n + s(n + n2)) work, where M(k) = o(k237) is the best known work bound for Jfc x ife matrix multiplication. The above bounds, with fi = 0.5, are applicable to planar graphs, since a fc05-separator decomposition can be computed within these bounds. We obtain further improvements for graphs with planar embeddings where all vertices lie on a small number of faces. The algorithm is based on augmenting G with a set of 0{n2fl) edges such that in the augmented graph, all distances can be obtained by paths of size O(logn).

关键词： Separators

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parallel construction of optimal alphabetic trees 93

Parallel construction of optimal alphabetic trees

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Proceedings of the 5th annual acm symposium on parallel algorithms and architectures

作者： Larmore, Lawrence Przytycka, M. Department of Computer Science University of California Riverside 92521 CA United States Department of Mathematics and Computer Science Odense University Odense M DK-5239 Denmark Institute of Informatics Warsaw University ul. Banacha 2 Warsaw 02-097 Poland

ISBN: (纸本)0897915992

A parallel algorithm is given which constructs an optimal alphabetic tree in 0(log3 n) time with n2 log n processors. The construction is basically a parallelization of the Garsia-Wachs version [5] of the Hu-tucker algorithm [8]. The best previous MC algorithm for the problem uses ra6/logn processors. [15] Our method is an extension of techniques used first in [3] and later used in [13] for the Huffman coding problem, which can be viewed as the alphabetic tree problem for the special case of a monotone weight sequence. In this paper, we extend to the case of certain "almost monotone" sequences, which we call "sorted regular valleys." The processing of such subsequences depends on a quadrangle inequality, while the total number of global iterations depends on a kind of tree contraction. Altogether we can view our algorithmic approach as (quadrangle inequality + tree contraction). An optimal alphabetic tree is a special case of an optimal binary search tree where all the weights are in the leaves. Thus, the result gives a partial answer to the open problem posed in [3]: is there an AfC algorithm which can find an optimal binary search tree and which user processors for some ep > 0?

关键词： Forestry

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parallel construction and query of suffix trees for two-dimensional matrices 93

Parallel construction and query of suffix trees for two-dime...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Giancarlo, Raffaele Grossi, Roberto AT and T Bell Laboratories Murray HillNJ07974 United States University of Palermo Italy Dipartimento di Informatica Università di Pisa Pisa56125 Italy Dipartimento di Sistemi e Informatica Università di Firenze Firenze50134 Italy

ISBN: (纸本)0897915992

We give efficient CRCW PRAM algorithms for the construction of two data structures, the Lsuffix Tree of a square matrix and the Nested Suffix Tree of a general matrix. The Lsuffix tree, introduced by Giancarlo [11], represents all square submatrices of a square matrix. The nested suffix tree, introduced here, represents all rectangular submatrices of a given general matrix. Both data structures can be seen as a generalization to matrices of the suffix tree of a string [18]. We remark that the problem of building a tree data structure representing all rectangular submatrices of a given matrix has been shown to be computationally harder than the problem of building a tree data structure representing only the square submatrices of a given matrix [10]. Thus, our attention for the important special case of square submatrices is justified. Once those two data structures are available, we can answer quickly and in parallel, a wide variety of queries that have many important applications in low-level image processing [20], visual databases [12] and two-dimensional data compression [16, 21, 22]. All matrices in this abstract have entries defined over an ordered alphabet E. © 1993 acm.

关键词： Matrix algebra

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Highly efficient dictionary matching in parallel 93

Highly efficient dictionary matching in parallel

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Muthukrishnan, S. Palem, K. Courant Institute of Mathematical Sciences 251 Mercer Street New YorkNY10012-1185 United States IBM Research Division T. J. Watson Research Center P. O. Box 704 Yorktown HeightsNY10598 United States

ISBN: (纸本)0897915992

We present highly efficient parallel algorithms for several well-studied dictionary matching problems. Our algorithms are faster and more efficient in terms of their parallel work, compared to previously known results. For static dictionary matching, we present an algorithm that preprocesses the dictionary and matches the text in O(logm) parallel time and 0(M + n log m) work, given any dictionary of size M whose longest pattern is m characters long, and a text of size n. We have further improved this algorithm to solve static dictionary matching with only 0((M + n)vlog m) work, if the characters are drawn from an alphabet of constant size. A distinguishing feature of these algorithms and the one stated below for matching in higher dimensions, is that in contrast with previous work, the running times, and work overheads when applicable, are dependent only on the length of the longest pattern m. We present a parallel algorithm for d-dimensional dictionary matching that runs in O(logm) time and matches the text in 0(M + nlogm) work for any fixed d. We present a new and more efficient parallel algorithm for dynamic dictionary matching. Insertions into and deletions from the dictionary, as well as matching the text can be done with optimal speedup in 0(A log M) work and 0(log M) time. Here, A denotes the length of the string to be inserted, deleted or matched into a dictionary of size M. All of the above algorithms are designed by applying the shrink-and-spawn technique that we introduce in this paper. We also show that this technique leads to parallel algorithms that only do optimal (linear) work, for multi-dimensional pattern matching and related problems [KLP89,Rab93]. Our algorithms are deterministic, as those in [KLP89], but however, are much simpler and preserve the efficiency as well as the speed of those presented there. © 1993 acm.

关键词： parallel algorithms

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Asymptotically tight bounds for performing BMMC permutations on parallel disk systems 93

Asymptotically tight bounds for performing BMMC permutations...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Cormen, Thomas H. Wisniewski, Leonard F. Department of Mathematics and Computer Science Dartmouth College United States

ISBN: (纸本)0897915992

We give asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform BMMC permutations (defined by a characteristic matrix that is nonsingular over GF{2)) on parallel disk systems. Under the Vitter-Shriver parallel-disk model with N records, D disks, block size B, and M records of RAM, we show a universal lower bound of Q (l + j)) parallel I/Os for performing a BMMC permutation, where 7 is the lower left lg(N/B) xlgB submatrix of the characteristic matrix. We adapt this lower bound to show that the algorithm for BPC permutations in [Cor93] is asymptotically optimal. We also present an algorithm that uses at most h (6 [is(m/b)1 + 5) parallel I/Os, which asymptotically matches the lower bound and improves upon the BMMC algorithm in [Cor93]. When rank(7) is low, this method is an improvement over the general-permutation bound of Although many BMMC permutations of practical interest fall into subclasses that might be explicitly invoked within the source code, we show how to detect in at most N/BD+ ['SW/H1] parallel I/Os whether a given vector of target addresses specifies a BMMC permutation. Thus, one can determine efficiently at run time whether a permutation to be performed is BMMC and then avoid the general-permutation algorithm and save parallel I/Os by using our algorithm. © 1993 acm.

关键词： Matrix algebra

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A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer 93

A doubly logarithmic communication algorithm for the complet...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Goldberg, Leslie Ann Jerrum, Mark Leighton, Tom Rao, Satish Sandia National Labs Department 1423 PO Box 5800 AlbuquerqueNM87185 United States University of Edinburgh Department of Computer Science King's Buildings EdinburghEH9 3JZ United Kingdom MIT Mathematics Department Laboratory for Computer Science CambridgeMA02139 United States NEC Research Institute 4 Independence Way PrincetonNJ08540 United States

ISBN: (纸本)0897915992

In this paper we consider the problem of interprocessor communication on a Completely Connected Optical Communication parallel Computer (OCPC). The particular problem we study is that of realizing an h-relation. In this problem, each processor has at most h messages to send and at most h messages to receive. It is clear that any 1-relation can be realized in one communication step on an OCPC. However, the best known p-processor OCPC algorithm for realizing an arbitrary h-relation for h > 1 requires Q(h + logp) expected communication steps. (This algorithm is due to Valiant and is based on earlier work of Anderson and Miller.) Valiant's algorithm is optimal only for h-fì(logp) and it is an open question of Geréb-Graus and Tsantilas whether there is a faster algorithm for h-o(logp). In this paper we answer this question in the affirmative by presenting a 0(/ì 4-log log p) communication step randomized algorithm that realizes an arbitrary h-relation on a p-processor OCPC. We show that if h © 1993 acm.

关键词： Optical communication

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parallel and output sensitive algorithms for combinatorial and linear algebra problems 93

Parallel and output sensitive algorithms for combinatorial a...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Cheriyan, Joseph Reif, John H. Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Department of Computer Science Duke University DurhamNC27706 United States

ISBN: (纸本)0897915992

The notion of output sensitive parallel algorithms for linear algebra problems is formalized in this paper, and such algorithms are presented for finding the rank of an n x n matrix in randomized parallel time 0(log n + logR) using 0(n2 + M(R)) processors, and for finding a maximum linearly independent subset of an n-set of n-dimensional vectors in randomized parallel time 0((log n) log3 R) using (n2 + RM(R)) processors (R is the size of the subset). Also, output sensitive TLSfC algorithms for some combinatorial problems are developed. The best TLSfC algorithm known for finding a maximum linearly independent subset of an n-set of n-dimensional vectors is given;the randomized parallel time is 0(logn) using 0(M(n)) processors. Note that this problem is likely harder than the problem of rinding a basis for the space spanned by the input vectors. An output sensitive TUfC algorithm for computing greatest common divisors of polynomials is developed. This result is due to the second author. A minimum vertex cover in a bipartite graph and a minimum X-Y vertex separator in a digraph can be found in randomized parallel time 0(log3 n) using 0(M(n)) processors (n is the number of vertices). This result is due to the first author. Note that this is the best complexity bound known for TLhfC algorithms, and matches the best TLSfC complexity bounds for the associated decision problems. © 1993 acm.

关键词： Graph theory

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Static single assignment for explicitly parallel programs 93

Static single assignment for explicitly parallel programs

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20th annual acm SIGPLAN-SIGACT symposium on Principles of Programming Languages, POPL'93

作者： Srinivasan, Harini Hook, James Wolfe, Michael Oregon Graduate Inst of Science and Technology Beaverton OR United States

ISBN: (纸本)0897915607

We describe and prove algorithms to convert programs which use the parallel Computing Forum parallel Sections construct into Static Single Assignment (SSA) form. This process allows compilers to apply classical scalar optimization algorithms to explicitly parallel programs. To do so, we must define what the concept of dominator and dominance frontier mean in parallel programs. We also describe how we extend SSA form to handle parallel updates and still preserve the SSA properties.

关键词： Computer software

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Fault diagnosis in a small constant number of parallel testing rounds 93

Fault diagnosis in a small constant number of parallel testi...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Beigel, Richard Margulis, Grigorii Spielman, Daniel A. Yale University United States Russian Academy of Sciences Russia MIT Russia Yale Station Department of Computer Science P.O. Box 2158 New HavenCT06520-2158 United States Department of Mathematics Yale Station P.O. Box 2155 New HavenCT06520-2155 United States Department of Applied Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States

ISBN: (纸本)0897915992

Consider a set of processors, V, that can communicate with each other. Assume that each processor can be either "good" or "faulty". Also assume that the processors can be used to test each other. We provide a parallel algorithm that determines which processors are good and which are faulty in 32 rounds of testing, provided that a strict majority of the processors are good. © 1993 acm.

关键词： parallel processing systems

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MIMD rendering algorithm for distributed memory architectures

MIMD rendering algorithm for distributed memory architecture...

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Proceedings of the 1993 parallel Rendering symposium

作者： Crockett, Thomas W. Orloff, Tobias Inst for Computer Applications in Science and Engineering

ISBN: (纸本)0818649208

We present a parallel rendering algorithm targeted to MIMD distributed-memory message-passing architectures. For maximum performance, the algorithm exploits both object-level and image-level parallelism. The behavior of the algorithm is examined both analytically and experimentally. The results show that the choice of message size has a significant impact on performance. Scalability to large numbers of processors is found to be limited primarily by communication overheads. An experimental implementation for the Intel iPSC/860 confirms the analytical results and demonstrates increasing performance from 1 to 128 processors across a wide range of scene complexities.

关键词： algorithms

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