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High-probability parallel transitive closure algorithms 90

High-probability parallel transitive closure algorithms

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SPAA '90 - Proceedings of the 2nd annual acm symposium on parallel algorithms and architectures

作者： Ullman, Jeffrey D. Yannakakis, Mihalis Stanford Univ Stanford KY United States

ISBN: (纸本)0897913701

The authors address the apparently difficult problem of doing parallel transitive closure when the (directed) graph is sparse and/or, only single-source information is desired. O(e) work is their target for the single-source problem. When the graph is sparse, then the all-pairs transitive closure problem can be solved by performing a depth-first search from each node, taking O(ne) time;that is their target for the all-pairs problem. The authors do not reach either target, except for the all-pairs case when e is fairly large. However, they make significant progress, in the sense that they have the first algorithms that simultaneously use time much less than linear and use work that is less than M(n).

关键词： Computer programming

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parallel scheduling of complex dags under uncertainty 05

Parallel scheduling of complex dags under uncertainty

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Seventeenth annual acm symposium on parallelism in algorithms and architectures

作者： Malewicz, Grzegorz Department of Computer Science University of Alabama Tuscaloosa AL 35487 United States Division of Mathematics and Computer Science Argonne National Laboratory Argonne IL 60439 United States

ISBN: (纸本)9781581139860

This paper introduces a parallel scheduling problem where a directed acyclic graph modeling t tasks and their dependencies needs to be executed on n unreliable workers. Worker i executes task j correctly with probability p i,j. The goal is to find a regimen Σ, that dictates how workers get assigned to tasks (possibly in parallel and redundantly) throughout execution, so as to minimize expected completion time. This fundamental parallel scheduling problem arises in grid computing and project management fields, and has several practical applications. We show a polynomial time algorithm for the problem restricted to the case when dag width is at most a constant and the number of workers is also at most a constant. These two restrictions may appear to be too severe. However, they are fundamentally required. Specifically, we demonstrate that the problem is NP-hard with constant number of workers when dag width can grow, and is also NP-hard with constant dag width when the number of workers can grow. When both dag width and the number of workers are unconstrained, then the problem is inapproximable within factor less than 5/4, unless P=NP. Copyright 2005 acm.

关键词： parallel processing systems

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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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parallel Sparse Matrix-Vector and Matrix-Transpose-Vector Multiplication Using Compressed Sparse Blocks 09

Parallel Sparse Matrix-Vector and Matrix-Transpose-Vector Mu...

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21st acm symposium on parallelism in algorithms and architectures

作者： Buluc, Aydin Fineman, Jeremy T. Frigo, Matteo Gilbert, John R. Leiserson, Charles E. Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA

ISBN: (纸本)9781605586069

This paper introduces a storage format for sparse matrices, called compressed sparse blocks (CSB), which allows both Ax and A(x)(inverted perpendicular) to be computed efficiently in parallel, where A is an n x n sparse matrix with nnz >= n nonzeros and x is a dense n-vector. Our algorithms use Theta(nnz) work (serial running time) and Theta(root nlgn) span (critical-path length), yielding a parallelism of Theta(nnz/root nlgn), which is amply high for virtually any large matrix. The storage requirement for CSB is esssentially the same as that for the more-standard compressed-sparse-rows (CSR) format, for which computing Ax in parallel is easy but A(x)(inverted perpendicular) is difficult. Benchmark results indicate that on one processor, the CSB algorithms for Ax and A(x)(inverted perpendicular) run just as fast as the CSR algorithm for Ax, but the CSB algorithms also scale up linearly with processors until limited by off-chip memory bandwidth.

关键词： Compressed sparse blocks compressed sparse columns compressed sparse rows matrix transpose matrix-vector multiplication multithreaded algorithm parallelism span sparse matrix storage format work

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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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Brief announcement: Between all and nothing-versatile aborts in hardware transactional memory

Brief announcement: Between all and nothing-versatile aborts...

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25th acm symposium on parallelism in algorithms and architectures, SPAA 2013

作者： Diestelhorst, Stephan Fetzer, Christof Spear, Michael Nowack, Martin TU Dresden Germany Lehigh University Bethlehem PA United States

ISBN: (纸本)9781450315722

Hardware Transactional Memory (HTM) implementations are becoming available in commercial, off-the-shelf components. While generally comparable, some implementations deviate from the strict all-or-nothing property of pure Transactional Memory. We analyse these deviations and find that with small modifications, they can be used to accelerate and simplify both transactional and nontransactional programming constructs. At the heart of our extensions we enable access to the transaction's full register state in the abort handler in an existing HTM without extending the architectural register state. Access to the full register state enables applications in both transactional and non-transactional parallel programming: hybrid transactional memory;transactional escape actions;transactional suspend/resume;and alert-on-update.

关键词： parallel programming

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A simple load balancing scheme for task allocation in parallel machines 91

A simple load balancing scheme for task allocation in parall...

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3rd annual acm symposium on parallel algorithms and architectures, SPAA 1991

作者： Rudolph, Larry Slivkin-Allalouf, Miriam Upfal, Eli Department of Computer Science Hebrew University Jerusalem Israel IBM TJ Watson Research Center Yorktown HeightsNY United States John Bryce Ltd. Science Based Industries PO BOX 23838 Jerusalem Israel Department of Applied Mathematics Weizman Institute Rehovot Israel IBM Almaden Research Center San JoseCA United States

ISBN: (纸本)0897914384

A collection of local workpiles (task queues) and a simple load balancing scheme is well suited for scheduling tasks in shared memory parallel machines. Task scheduling on such machines has usually been done through a single, globally accessible, workpile. The scheme introduced in this paper achieves a balancing comparable to that of a global workpile, while minimizing the overheads. In many parallel computer architectures, each processor has some memory that it can access more efficiently, and so it is desirable that tasks do not mirgrate frequently. The load balancing is simple and distributed: Whenever a processor accesses its local workpile, it performs a balancing operation with probability inversely proportional to the size of its workpile. The balancing operation consists of examining the workpile of a random processor and exchanging tasks so as to equalize the size of the two workpiles. The probabilistic analysis of the performance of the load balancing scheme proves that each tasks in the system receives its fair share of computation time. Specifically, the expected size of each local task queue is within a small constant factor of the average, i.e. total number of tasks in the system divided by the number of processors. © 1991 acm.

关键词： Memory architecture

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Optimal Round and Sample-Size Complexity for Partitioning in parallel Sorting 23

Optimal Round and Sample-Size Complexity for Partitioning in...

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35th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Yang, Wentao Harsh, Vipul Solomonik, Edgar Univ Illinois Dept Comp Sci Urbana IL 61801 USA

ISBN: (纸本)9781450395458

State-of-the-art parallel sorting algorithms for distributed-memory architectures are based on computing a balanced partitioning via sampling and histogramming. By finding samples that partition the sorted keys into evenly-sized chunks, these algorithms minimize the number of communication rounds required. Histogramming (computing positions of samples) guides sampling, enabling a decrease in the overall number of samples collected. We derive lower and upper bounds on the number of sampling/histogramming rounds required to compute a balanced partitioning. We improve on prior results to demonstrate that when using p processors, O(log* p) rounds with O(p/log* p) samples per round suffice. We match that with a lower bound that shows that any algorithm with O(p) samples per round requires at least Omega(log* p) rounds. Additionally, we prove the Omega(p log p) samples lower bound for one round, thus proving that existing one round algorithms: sample sort, AMS sort [2] and HSS [16] have optimal sample size complexity. To derive the lower bound, we propose a hard randomized input distribution and apply classical results from the distribution theory of runs.

关键词： parallel algorithms parallel sorting communication cost communication lower bounds

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parallel equivalence class sorting: algorithms, lower bounds, and distribution-based analysis 16

Parallel equivalence class sorting: Algorithms, lower bounds...

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28th acm symposium on parallelism in algorithms and architectures, SPAA 2016

作者： Devanny, William E. Goodrich, Michael T. Jetviroj, Kristopher Dept. of Computer Science Univ. of California Irvine IrvineCA92697 United States

ISBN: (纸本)9781450342100

We study parallel comparison-based algorithms for finding all equivalence classes of a set of n elements, where sorting according to some total order is not possible. Such scenarios arise, for example, in applications, such as in distributed computer security, where each of n agents are working to identify the private group to which they belong, with the only operation available to them being a zero-knowledge pairwise-comparison (which is sometimes called a "secret handshake") that reveals only whether two agents are in the same group or in different groups. We provide new parallel algorithms for this problem, as well as new lower bounds and distribution-based analysis.

关键词： Equivalence classes

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parallel continuous randomized load balancing

Parallel continuous randomized load balancing

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Proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Berenbrink, P. Friedetzky, T. Mayr, E.W. Paderborn Univ Paderborn Germany

Recently, the subject of allocating tasks to servers has attracted much attention. There are several ways of distinguishing load balancing problems. There are sequential and parallel strategies, that is, placing the tasks one after the other or all of them in parallel. Another approach divides load balancing problems into continuous and static ones. In the continuous case new tasks are generated and consumed as time proceeds, in the second case the number of tasks is fixed. We present and analyze a parallel randomized continuous load balancing algorithm in a scenario where n processors continuously generate and consume tasks according to some given probability distribution. Each processor initiates load balancing actions only if its load exceeds a certain threshold t, and then tries to find a balancing partner for moving some of its tasks to this partner. We consider several randomized load generation and consumption schemes which yield an expected load of O(n) in the whole system. We show that the maximum load of any processor is upper bounded by (log log n)2, with high probability. The expected number of load requests required for finding a balancing partner is constant.

关键词： parallel algorithms

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