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Optimal parallel construction of Hamiltonian cycles and spanning trees in random graphs 93

Optimal parallel construction of Hamiltonian cycles and span...

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

作者： MacKenzie, Philip D. Stout, Quentin F. Advanced Computer Architecture Laboratory Department of Electrical Engineering and Computer Science University of Michigan Ann ArborMI48109-2122 United States

ISBN: (纸本)0897915992

We give tight bounds on the parallel complexity of some problems involving random graphs. Specifically, we show that a Hamiltonian cycle, a breadth first spanning tree, and a maximal matching can all be constructed in (logn) expected time using n/lognprocessors on the CRCW PRAM. This is a substantial improvement over the best previous algorithms, which required ((log log n)2) time and nlog2n processors. We then introduce a technique which allows us to prove that constructing an edge cover of a random graph from its adjacency matrix requires (logn) expected time on a CRCW PRAM with O(n) processors. Constructing an edge cover is implicit in constructing a spanning tree, a Hamiltonian cycle, and a maximal matching, so this lower bound holds for all these problems, showing that our algorithms are optimal. This new lower bound technique is one of the very few lower bound techniques known which apply to randomized CRCW PRAM algorithms, and it provides the first nontrivial parallel lower bounds for these problems. © 1993 acm.

关键词： Hamiltonians

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An efficient parallel algorithm for the single function coarsest partition problem 93

An efficient parallel algorithm for the single function coar...

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

作者： JáJá, Joseph F. Ryu, Kwan Woo Department of Electrical Engineering Institute for Systems Research Korea Republic of Department of Computer Engineering Kyungpook National University Daegu Korea Republic of Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

ISBN: (纸本)0897915992

We describe an efficient parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O(logn) time using 0(n log log n) operations on the Arbitrary CRCW PRAM. The previous best known algorithm runs in 0(log2 n) time using 0(n log2 n) operations on the CREW PRAM. Another algorithm developed independently of ours runs in O(logn) time using 0(n log n) operations on the Arbitrary CRCW PRAM. Our solution is based on efficient algorithms for solving several subproblems that are of independent interest. In particular, we present efficient parallel algorithms to find a minimal starting point of a circular string with respect to lexicographic ordering and to sort lexicographically a list of strings of different lengths. © 1993 acm.

关键词： parallel algorithms

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Experience in massively parallel discrete event simulation 93

Experience in massively parallel discrete event simulation

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

作者： Greenberg, Albert G. Lubachevsky, Boris D. Wang, Li-Chung AT and T Bell Laboratories United States University of Texas Austin United States

ISBN: (纸本)0897915992

Discrete event simulation of complex systems is one of the most important problems in scientific and industrial computing. It is not uncommon for a single simulation run to take hours on a high speed workstation. Massively parallel computers provide opportunities for simulating complex systems significantly faster. At the heart of the computational difficulties in parallel simulation are (i) random, data-dependent events that couple subsystems, and (ii) asymmetries wherein some subsystems receive a disproportionate number of events, leading to severe load imbalances. In this paper, we discuss a parallel simulation of a complex system-a large asymmetric circuit-switched network, with state-dependent control-and methods we have apphed to overcome both types of difficulties just mentioned. In a worst case sense, we show that the problem is hard: In particular, simulation of a network with just three nodes is P-complete. However, we show that a general purpose synchronous relaxation method uncovers the parallelism inherent in practical, realistic cases. In addition, we show that special purpose (specific to circuit-switched simulations) parallel methods allow us to profitably assign more processors to subsystems receiving more events, and thereby handle load imbalances. Promising performance results are reported for a 16384 processor MasPar MP-1 implementation, on a realistic 114 node network simulation scenario. © 1993 acm.

关键词： Discrete event simulation

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A dynamic distributed load balancing algorithm with provable good performance 93

A dynamic distributed load balancing algorithm with provable...

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

作者： Lüling, Reinhard Monien, Burkhard Department of Mathematics and Computer Science University of Paderborn Germany

ISBN: (纸本)0897915992

The overall efficiency of parallel algorithms is most decisively effected by the strategy applied for the mapping of workload. Strategies for balancing dynamically generated workload on a processor network which are also useful for practical applications have intensively been investigated by simulations and by direct applications. This paper presents the complete theoretical analysis of a dynamically distributed load balancing strategy. The algorithm is adaptive by nature and is therefore useful for a broad range of applications. A similar algorithmic principle has already been implemented for a number of applications in the areas of combinatorial optimization, parallel programming languages and graphical animation. The algorithm performed convincingly for all these applications. In our analysis we will prove that the expected number of packets on each processor varies only by a constant factor compared with that on any other processor, independent of the generation and consumption of workload on each processor. We give exact bounds for these values and prove an exact upper bound, independent of the number of processors. Thus, the algorithm achieves a well-balanced workload distribution on any network for any underlying application. We also prove that the variation of the expected number of packets on a processor is very small and only dependent on the parameters of the algorithm. Furthermore, we present some analysis of the costs of our algorithm. We will also show that all tradeoffs between balancing quality, variation and costs can be determined by the parameters of the algorithm. © 1993 acm.

关键词： parallel programming

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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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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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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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