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Nearly Optimal parallel algorithms for Longest Increasing Subsequence 23

Nearly Optimal Parallel Algorithms for Longest Increasing Su...

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

作者： Cao, Nairen Huang, Shang-En Su, Hsin-Hao Boston Coll Boston MA 02467 USA

ISBN: (纸本)9781450395458

The paper presents parallel algorithms for multiplying implicit simple unit-Monge matrices (Krusche and Tiskin, PPAM 2009) of size n x n in the EREW PRAM model. We show implicit simple unit-Monge matrices multiplication of size nxn can be achieved by a deterministic EREW PRAM algorithm with O(n log n log log n) total work and O(log(3) n) span. This implies that there is a deterministic EREW PRAM algorithm solving the longest increasing subsequence (LIS) problem in O(n log(2) n log log n) work and O(log(4) n) span. Furthermore, with randomization and bitwise operations, implicitly multiplying two simple unit-Monge matrices can be improved to O(n log n) work and O(log(3) n) span, which leads to a randomized EREW PRAM algorithm obtaining LIS in O(n log(2) n) work and O(log(4) n) span with high probability. In the regime where the LIS has length k = Omega(log(3) n), our results improve the span from (O) over tilde (n(2/3)) (Krusche and Tiskin, SPAA 2010) and O(k log n) (Gu, Men, Shen, Sun, and Wan, SPAA 2023) to O(log(4) n) while the total work remains near optimal (O) over tilde (n).

关键词： Longest increasing subsequence Implicit simple unit-Monge matrix multiplication parallel algorithm

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Low-contention depth-first scheduling of parallel computations with write-once synchronization variables 01

Low-contention depth-first scheduling of parallel computatio...

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13th annual symposium on parallel algorithms and architectures (SPAA 2001)

作者： Fatourou, P. Department of Computer Science University of Toronto Toronto Ont. Canada

ISBN: (纸本)9781581134094

We present an efficient, randomized, online, scheduling algorithm for a large class of programs with write-once synchronization variables. The algorithm combines the work-stealing paradigm with the depth-first scheduling technique, resulting in high space efficiency and good time complexity. By automatically increasing the granularity of the work scheduled on each processor, our algorithm achieves good locality, low contention and low scheduling overhead, improving upon a previous depth-first scheduling algorithm [6] published in SPAA'97. Moreover, it is provably efficient for the general class of multithreaded computations with write-once synchronization variables (as studied in [6]), improving upon algorithm DFDeques (published in SPAA'99 [24]), which is only for the more restricted class of nested parallel computations. More specifically, consider such a computation with work T1, depth T∞ and σ synchronization, and suppose that space S1 suffices to execute the computation on a single-processor computer. Then, on a P-processor shared-memory parallel machine, the expected space complexity of our algorithm is at most S1 + O(PT∞ log(PT∞)), and its expected time complexity is O(T1/P+σlog(PT∞)/P+T∞ log(PT∞)). Moreover, for any Ε > 0, the space complexity of our algorithm is S1 + O(P(T∞ + ln(1/Ε))log(P(T∞ + ln(P(T∞ + ln(1/Ε))/Ε)))) with probability at least 1 - Ε. Thus, even for values of Ε as small as e -T∞, the space complexity of our algorithm is at most S1 + O(PT∞ log(PT∞)) with probability at least 1 - e-T∞. These bounds include all time and space costs for both the computation and the scheduler.

关键词： parallel processing systems

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Windows scheduling of arbitrary length jobs on parallel machines 05

Windows scheduling of arbitrary length jobs on parallel mach...

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Seventeenth annual acm symposium on parallelism in algorithms and architectures

作者： Bar-Noy, Amotz Ladner, Richard E. Tamir, Tami VanDegrift, Tammy Computer and Information Science Department Brooklyn College 2900 Bedford Ave. Brooklyn NY 11210 Department of Computer Science and Engineering Box 352350 University of Washington Seattle WA 98195 School of Commiter Science Interdisciplinary Center Herzliya Israel Electrical Engineering and Computer Science University of Portland 5000 N. Willamette Blvd. Portland OR 97203

ISBN: (纸本)9781581139860

The generalized windows scheduling problem for n jobs on multiple machines is defined as follows: Given is a sequence, I = 〈(w1, l 1),(w2, l2),....(wn, l n)〉 of n Pairs of positive integers that are associated with the jobs 1, 2,..., n, respectively. The processing length of job i is li slots (a slot is the processing time of one length unit). The goal is to repeatedly and non-preemptively schedule all the jobs on the fewest possible parallel machines such that the gap (window) between two consecutive executions of the first slot of. job i is at most wi slots. This problem arises in push broadcast systems in which data is transmitted on parallel channels. The problem is NP-hard even for unit-length jobs and a (1 + Ε)-approximation algorithm is known for this case by approximating the natural lower bound W(I) = Σi=1n(1/wi). The techniques used for approximating unit-length jobs cannot be applied for arbitrary-length jobs mainly because the optimal number of machines might be arbitrarily larger than the generalized lower bound W (I) = Σi=1n(l i/wi). Our main result is an 8-approximation algorithm for the generalized problem using new methods, different from those used for the unit-length case. We also present an algorithm that uses 2(1 + Ε)W(I) + log wmax machines and a greedy algorithm that is based on a new tree representation of schedules. The greedy algorithm is optimal for some special and simulations show that it performs very well in practice. Copyright 2005 acm.

关键词： parallel processing systems

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Simple parallel algorithms for Single-Site Dynamics 2022

Simple Parallel Algorithms for Single-Site Dynamics

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54th annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Liu, Hongyang Yin, Yitong Nanjing Univ State Key Lab Novel Software Technol Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781450392648

The single-site dynamics are a canonical class of Markov chains for sampling from high-dimensional probability distributions, e.g. the ones represented by graphical models. We give a simple and generic parallel algorithm that can faithfully simulate single-site dynamics. When the chain asymptotically satisfies the l(p) -Dobrushin's condition, specifically, when the Dobrushin's influence matrix has constantly bounded l(p)-induced operator norm for an arbitrary p epsilon [1, 8], the parallel simulation of.. steps of single-site updates succeeds within Omicron (Nu / n + log n) depth of parallel computing using (O) over tilde (m) processors, where n is the number of sites and.. is the size of graphical model. Since the Dobrushin's condition is almost always satisfied asymptotically by mixing chains, this parallel simulation algorithm essentially transforms single-site dynamics with optimal o (n log n) mixing time to RNC algorithms for sampling. In particular we obtain RNC samplers, for the Ising models on general graphs in the uniqueness regime, and for satisfying solutions of CNF formulas in a local lemma regime. With non-adaptive simulated annealing, these RNC samplers can be transformed routinely to RNC algorithms for approximate counting. A key step in our parallel simulation algorithm, is a so-called "universal coupling" procedure, which tries to simultaneously couple all distributions over the same sample space. We construct such a universal coupling, that for every pair of distributions the coupled probability is at least their Jaccard similarity. We also prove that this is optimal in the worst case. The universal coupling and its applications are of independent interests.

关键词： Single-site dynamics Markov chain Monte Carlo sampling

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Adaptive Massively parallel algorithms for Cut Problems 22

Adaptive Massively Parallel Algorithms for Cut Problems

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Hajiaghayi, MohammadTaghi Knittel, Marina Olkowski, Jan Saleh, Hamed Univ Maryland College Pk MD 20742 USA

ISBN: (纸本)9781450391467

We study the Weighted Min Cut problem in the Adaptive Massively parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively parallel Computation (MPC) model. In the past decade, research on highly scalable algorithms has had significant impact on many massive systems. The MPC model, introduced in 2010 by Karloff et al. [16], which is an abstraction of famous practical frameworks such as MapReduce, Hadoop, Flume, and Spark, has been at the forefront of this research. While great strides have been taken to create highly efficient MPC algorithms for a range of problems, recent progress has been limited by the 1-vs-2 Cycle Conjecture [20], which postulates that the simple problem of distinguishing between one and two cycles requires Omega( log n) MPC rounds. In the AMPC model, each machine has adaptive read access to a distributed hash table even when communication is restricted (i.e., in the middle of a round). While remaining practical [4], this gives algorithms the power to bypass limitations like the 1-vs-2 Cycle Conjecture. We give the first sublogarithmic AMPC algorithm, requiring O(log logn) rounds, for (2 + epsilon)-approximate weighted Min Cut. Our algorithm is inspired by the divide and conquer approach of Ghaffari and Nowicki [11], which solves the ( 2 +epsilon)-approximate weighted Min Cut problem in O ( log n log log n) rounds of MPC using the classic result of Karger and Stein [15]. Our work is fullyscalable in the sense that the local memory of each machine is O(n(epsilon)) for any constant 0 < epsilon < 1. There are no o(logn)-round MPC algorithms for Min Cut in this memory regime assuming the 1-vs-2 Cycle Conjecture holds. The exponential speedup in the AMPC runtime is the result of decoupling the different layers of the divide and conquer algorithm and solving all layers in O (1) rounds in parallel. Finally, we extend our approach: we present an O (kappa log log n)-round AMPC algorithms fo

关键词： Massively parallel Computation minimum cut adaptivity

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The effect of communication costs in solid-state quantum computing architectures 03

The effect of communication costs in solid-state quantum com...

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Fifteenth annual acm symposium on parallelism in algorithms and architectures

作者： Copsey, Dean Oskin, Mark Metodiev, Tzvetan Chong, Frederic T. Chuang, Isaac Kubiatowicz, John University of Washington Seattle WA United States University of California at Davis Davis CA United States University of California Berkeley Berkeley CA United States

ISBN: (纸本)9781581136616

Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: the short spatial distance of quantum interactions and the short temporal life of quantum data. In particular, quantum computations must make use of extremely robust error correction techniques to extend the life of quantum data. We present optimized spatial layouts of quantum error correction circuits for quantum bits embedded in silicon. We analyze the complexity of error correction under the constraint that interaction between these bits is near neighbor and data must be propagated via swap operations from one part of the circuit to another. We discover two interesting results from our quantum layouts. First, the recursive nature of quantum error correction circuits requires a additional communication technique more powerful than near-neighbor swaps - too much error accumulates if we attempt to swap over long distances. We show that quantum teleportation can be used to implement recursive structures. We also show that the reliability of the quantum swap operation is the limiting factor in solid-state quantum computation.

关键词： Fault tolerant computer systems

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Scheduling best-effort and real-time pipelined applications on time-shared clusters 01

Scheduling best-effort and real-time pipelined applications ...

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13th annual symposium on parallel algorithms and architectures (SPAA 2001)

作者： Zhang, Y. Sivasubramaniam, A. Dept. of Computer Sci./Engineering Pennsylvania State University University Park PA 16802 United States

ISBN: (纸本)9781581134094

Two important emerging trends are influencing the design, implementation and deployment of high performance parallel systems. The first is on the architectural end, where both economic and technological factors are compelling the use of off-the-shelf computing elements (workstations/PCs and networks) to put together high performance systems called clusters. The second is from the user community that is finding an increasing number of applications to benefit from such high performance systems. Apart from the scientific applications that have traditionally needed supercomputing power, a large number of graphics, visualization, database, web service and e-commerce applications have started using clusters because of their high processing and storage requirements. These applications have diverse characteristics and can place different Quality-of-Service (QoS) requirements on the underlying system (low response time, high throughput, high I/O demands, guaranteed response/throughput etc.). Further, clusters run ning such applications need to cater to potentially a large number of users (or other applications) in a time-shared manner. The underlying system needs to accommodate the requirements of each application, while ensuring that they do not interfere with each other. This paper focuses on the CPU resources of a cluster and investigates scheduling mechanisms to meet the responsiveness, throughput and guaranteed service requirements of different applications. Specifically, we propose and evaluate three different scheduling mechanisms. These mechanisms have been drawn from traditional solutions on parallel systems (gang scheduling and dynamic coscheduling), and have been extended to accommodate the new criteria under consideration. These mechanisms have been investigated using detailed simulation and workload models to show their pros and cons for different performance metrics.

关键词： parallel processing systems

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A parallel Genetic algorithms Framework based on Hadoop MapReduce 15

A Parallel Genetic Algorithms Framework based on Hadoop MapR...

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30th acm symposium on Applied Computing (SAC)

作者： Ferrucci, Filomena Salza, Pasquale Kechadi, M-Tahar Sarro, Federica Univ Salerno Fisciano Sa Italy Univ Coll Dublin Dublin Ireland UCL London WC1E 6BT England

ISBN: (纸本)9781450331968

This paper describes a framework for developing parallel Genetic algorithms (GAs) on the Hadoop platform, following the paradigm of MapReduce. The framework allows developers to focus on the aspects of GA that are specific to the problem to be addressed. Using the framework a GA application has been devised to address the Feature Subset Selection problem. A preliminary performance analysis showed promising results.

关键词： Hadoop MapReduce parallel Genetic algorithms

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EFFICIENT parallel COMPUTATIONS FOR SINGULAR BAND MATRICES 6

EFFICIENT PARALLEL COMPUTATIONS FOR SINGULAR BAND MATRICES

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6th annual acm/SIAM symposium on Discrete algorithms

作者： EBERLY, W UNIV CALGARY DEPT COMP SCICALGARYAB T2N 1N4CANADA

ISBN: (纸本)0898713498

Efficient parallel algorithms are presented for singular band matrix computations over arbitrary fields - including solving systems of linear equations, and computation of the rank and a maximal nonsingular minor of a nonsingular band matrix. The algorithms are reasonably fast: for computations of band matrices of order n and band width m they are only an O(log m log² logn) factor slower than the fastest known algorithms for singular (or nonsingular) band matrix computations. As well, sequential implementations of the new algorithms are asymptotically faster than previous algorithms if an asymptotically efficient matrix multiplication algorithm is used as a subroutine.

关键词： Matrix algebra

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Weighted distributed hash tables 05

Weighted distributed hash tables

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Seventeenth annual acm symposium on parallelism in algorithms and architectures

作者： Schindelhauer, Christian Schomaker, Gunnar Heinz Nixdorf Institute Computer Science Department University of Paderborn Germany

ISBN: (纸本)9781581139860

We present two methods for weighted consistent hashing also known as weighted distributed hash tables. The first method, called Linear Method, combines the standard consistent hasing introduced by Karger et al. [9] with a linear weighted distance measure. By using node copies and different partitions of the hash space, the balance of this scheme approximates the fair weight relationship with high probability. The second method, called the Logarithmic Method, uses a logarithmic weighted distance between the peers and the data to find the corresponding node. For distributing one data element it provides perfect weighted balance. To provide this distribution for many data elements we use partitions to achieve a fair balance with high probability. These methods provide small fragmentation, which means that the hash space is divided into at most script O sign(n log n) intervals. Furthermore, there is an efficient data structure that assigns data elements to the nodes in expected time script O sign(log n). If small fragmentation is not an issue one can replace the use of partitions by a method we call double hash functions. This method needs script O sign(n) for assigning elements to a node, yet it can be directly used for Storage Area Networks, where the number of nodes is small compared to participating nodes in Peer-to-Peer networks. Copyright 2005 acm.

关键词： parallel processing systems

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