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Fast set operations using treaps 98

Fast set operations using treaps

引用

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

作者： Blelloch, G.E. Reid-Miller, M. Carnegie Mellon Univ Pittsburgh PA United States

ISBN: (纸本)9780897919890

We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (treaps [26]). For two sets of size n and m (m ≤ n) the algorithms run in expected O(m lg(n/m)) work and O(lg n) depth (parallel time) on an EREW PRAM with scan operations (implying O(lg2 n) depth on a plain EREW PRAM). As with the sequential algorithms on treaps for insertion and deletion the main advantage of our algorithms are their simplicity. In fact our algorithms for set operations seem simpler than previous sequential algorithms with the same work bounds, and might therefore also be useful in a sequential context. To analyze the effectiveness of the algorithms we implemented both sequential and parallel versions of the algorithms and ran several experiments on them. Our parallel implementation uses the Cilk [5] shared memory runtime system on a 16 processor SGI Power Challenge and a 6 processor Sun Ultra Enterprise 3000. It shows reasonable speedup: 6.3 to 6.8 speedup on 8 processors of the SGI, and 4.1 to 4.4 speedup on 5 processors of the Sun.

关键词： parallel algorithms

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Framework for simple sorting algorithms on parallel disk systems

Framework for simple sorting algorithms on parallel disk sys...

引用

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

作者： Rajasekaran, S. Univ of Florida Gainesville United States

In this paper we present a simple parallel sorting algorithm and illustrate two applications. The algorithm (called the (l, m)-merge sort (LMM)) is an extension of the bitonic and odd-even merge sorts. Literature on parallel sorting is abundant. Many of the algorithms proposed, though being theoretically important, may not perform satisfactorily in practice owing to large constants in their time bounds. The algorithm to be presented in this paper, due partly to its simplicity, results in small constants. We present an implementation for the parallel disk sorting problem. The algorithm is asymptotically optimal (assuming that N is a polynomial in M, where N is the number of records to be sorted and M is the internal memory size). The underlying constant is very small. This algorithm has a better performance than the disk-striped mergesort (DSM) algorithm when the number of disks is large. Our implementation is as simple as that of DSM (requiring no fancy data structures or prefetch techniques). As a second application, we prove that we can get a sparse enumeration sort on the hypercube that is simpler than that of the classical algorithm of Nassimi and Sahni. We also show that Leighton's columnsort algorithm is a special case of LMM.

关键词： parallel algorithms

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Automatic parallel I/O performance optimization in Panda 98

Automatic parallel I/O performance optimization in Panda

引用

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

作者： Chen, Y. Winslett, M. Cho, Y. Kuo, S. Univ of Illinois

ISBN: (纸本)9780897919890

parallel I/O systems typically consist of individual processors, communication networks, and a large number of disks. Managing and utilizing these resources to meet performance, portability and usability goals of applications has become a significant challenge. We believe that a parallel I/O system that automatically selects efficient I/O plans for user applications is a solution to this problem. In this paper, we present such an automatic performance optimization approach for scientific applications performing collective I/O requests on multidimensional arrays. Under our approach, an optimization engine in a parallel I/O system selects optimal I/O plans automatically without human intervention based on a description of the application I/O requests and the system configuration. To validate our hypothesis, we have built an optimizer that uses a rule-based and randomized search-based algorithms to select optimal parameter settings in Panda, a parallel I/O library for multidimensional arrays. Our performance results obtained from two IBM SPs with significantly different configurations show that the Panda optimizer is able to select high-quality I/O plans and deliver high performance under a variety of system configurations.

关键词： parallel algorithms

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parallel continuous randomized load balancing

Parallel continuous randomized load balancing

引用

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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Elimination forest guided 2D sparse LU factorization 98

Elimination forest guided 2D sparse LU factorization

引用

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

作者： Shen, K. Jiao, X. Yang, T. Univ of California Santa Barbara CA United States

ISBN: (纸本)9780897919890

Sparse LU factorization with partial pivoting is important for many scientific applications and delivering high performance for this problem is difficult on distributed memory machines. Our previous work has developed an approach called S* that incorporates static symbolic factorization, supernode partitioning and graph scheduling. This paper studies the properties of elimination forests and uses them to guide supernode partitioning/amalgamation and execution scheduling. The new design with 2D mapping effectively identifies dense structures without introducing too many zeros in the BLAS computation and exploits asynchronous parallelism with low buffer space cost. The implementation of this code, called S+, uses supernodal matrix multiplication which retains the BLAS-3 level efficiency and avoids unnecessary arithmetic operations. The experiments show that S+ improves our previous code substantially and can achieve up to 11.04GFLOPS on 128 Cray T3E 450 MHz nodes, which is the highest performance reported in the literature.

关键词： parallel algorithms

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Blocking in parallel multisearch problems (extended abstract) 98

Blocking in parallel multisearch problems (extended abstract...

引用

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

作者： Dittrich, W. Hutchinson, D. Maheshwari, A. Bosch Telecom GmbH Backnang Germany

ISBN: (纸本)9780897919890

External memory (EM) algorithms are designed for computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. Block-wise access to data is a central theme in the design of efficient EM algorithms. A similar requirement arises in the transmission of data between processors in certain parallel computation models such as BSP* and CGM, for which block-wise communication is a crucial issue. We consider multisearch problems, where a large number of queries are to be simultaneously processed and satisfied by navigating through large data structures on parallel computers. The examples used originate as BSP* algorithms and we adapt them to the EM situation where the queries and data structure are considered to be much larger than the size of the available internal memory. This paper presents techniques to achieve blocking for I/O as well as for communication in multisearch on the BSP* and EM-BSP* models. In the area of EM algorithms new algorithms for multisearch in balanced trees are described. For search trees up to size O(n log n) where n is the number of queries, we obtain work-optimal, parallel, EM multisearch algorithms whose I/O and communication time are the same, asymptotically, as the computation time. These algorithms are obtained via the simulation technique of [15]. For larger trees we describe a parallel, EM algorithm which is simultaneously c-optimal and I/O-optimal. We give a lower bound to the number of I/O operations required for filtering n queries through a binary or multiway search tree of size m when m ≥ n2+Ε, constant Ε > 0. In the domain of parallel, non-EM algorithms we describe a new 1-optimal algorithm for BSP* multisearch in optimal trees which communicates in a block-wise fashion.

关键词： parallel processing systems

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Communication-optimal parallel minimum spanning tree algorithms extended abstract

Communication-optimal parallel minimum spanning tree algorit...

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

作者： Adler, M. Dittrich, W. Juurlink, B. Kutylowski, M. Rieping, I. Univ of Toronto Toronto Ont Canada

Lower and upper bounds for finding a minimum spanning tree (MST) in a weighted undirected graph on the BSP model are presented. We provide the first non-trivial lower bounds on the communication volume required to solve the MST problem. Let p denote the number of processors, n the number of nodes of the input graph, and m the number of edges of the input graph. We show that in the worst case a total of Ω(k·min(m, pn)) bits need to be transmitted in order to solve the MST problem, where k is the number of bits required to represent a single edge weight. This implies that if each message contains k bits, any BSP algorithm for finding an MST requires communication time Ω(g · min(m/p, n)), where g is the gap parameter of the BSP model. In addition, we present two algorithms whose running times match the lower bounds in different situations. Both algorithms perform linear work and use a number of super-steps independent of the input size. The first algorithm is simple but can employ at most m/n processors efficiently. Hence, it should be applied in situations where the input graph is relatively dense. The second algorithm is a randomized algorithm that performs linear work with high probability, provided that m ≥ n · log p. This is the first linear work BSP algorithm for finding an MST in sparse graphs.

关键词： parallel algorithms

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Asynchronous shared memory search structures 96

Asynchronous shared memory search structures

引用

8th annual acm symposium on parallel algorithms and architectures

作者： Adler, M Univ Calif Berkeley Div Comp Sci Berkeley CA 94720 USA Int Comp Sci Inst Berkeley CA 94704 USA

ISBN: (纸本)9780897918091

We study the problem of storing an ordered E;et On an asynchronous shared memory parallel computer. We examine the case where we want to perform successor (least upper bound) queries efficiently on the set members that are stored. We also examine the case where processors insert and delete members of the set. Due to asynchrony, we require processors to perform queries and to maintain the structure independently. Although several such structures have been proposed, the analysis of these structures has been very limited. We here ut;e the recently proposed QRQW PRAM model to provide upper and lower bounds on the performance of such data structures. In the asynchronous QRQW PRAM, the problem of processors concurrently and independently searching a shared data structure is very similar to the problem of routing packets through a network. Using this as a guide, we introduce the Search-Butterfly, a search structure that combines the efficient packet routing properties of the butterfly graph with the efficient search structure properties of the B-Tree. We analyze the behavior of the Search-Butterfly when the following operations are performed: arbitrary searches, random searches,and random searches, insertions, and deletions. We also provide lower bounds that show that the results are within a factor of O (log n) of optimal where n is the number of keys;in the structure. When the searches are random, the results are within a constant factor of optimal. Many of the proofs are derived from closely related results for packet routing. Others are of independent interest, most notably a method of adding queues to any network belonging to a large class of queuing networks with non-Markovian routing in a manner that allows us to bound the delay experienced by packets in the augmented network.

关键词： parallel processing systems

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Detecting data races in Cilk programs that use locks 98

Detecting data races in Cilk programs that use locks

引用

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

作者： Cheng, G.-I. Feng, M. Leiserson, Ch.E. Randall, K.H. Stark, A.F. MIT Lab for Computer Science Cambridge MA United States

ISBN: (纸本)9780897919890

When two parallel threads holding no locks in common access the same memory location and at least one of the threads modifies the location, a 'data race' occurs, which is usually a bug. This paper describes the algorithms and strategies used by a debugging tool, called the Nondeterminator-2, which checks for data races in programs coded in the Cilk multithreaded language. Like its predecessor, the Nondeterminator, which checks for simple 'determinacy' races, the Nondeterminator-2 is a debugging tool, not a verifier, since it checks for data races only in the computation generated by a serial execution of the program on a given input. We give an algorithm, ALL-SETS, that determines whether the computation generated by a serial execution of a Cilk program on a given input contains a race. For a program that runs serially in time T, accesses V shared memory locations, uses a total of n locks, and holds at most k n locks simultaneously, ALL-SETS runs in. O(nkT α(V, V)) time and O(nkV) space, where α is Tarjan's functional inverse of Ackermann's function. Since ALL-SETS may be too inefficient in the worst case, we propose a much more efficient algorithm which can be used to detect races in programs that obey the 'umbrella' locking discipline, a programming methodology that is more flexible than similar disciplines proposed in the literature. We present an algorithm, BRELLY, which detects violations of the umbrella discipline in O(kT α(V, V)) time using O(kV) space. We also prove that any 'abelian' Cilk program, one whose critical sections commute, produces a determinate final state if it is deadlock free and if it generates any computation which is data-race free. Thus, the Nondeterminator-2's two algorithms can verify the determinacy of a deadlock-free abelian program running on a given input.

关键词： parallel algorithms

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Dynamic scheduling with incomplete information 98

Dynamic scheduling with incomplete information

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

作者： Bast, H. Max-Planck-Inst fur Informatik Saarbrucken Germany

ISBN: (纸本)9780897919890

We consider the following scheduling problem: Our goal is to execute a given amount of arbitrarily decomposable work on a distributed machine as quickly as possible. The work is maintained by a central scheduler that can assign chunks of work of an arbitrary size to idle processors. The difficulty is that the processing time required for a chunk is not exactly predictable - usually the less, the larger the chunk - and that processors suffer a delay for each assignment. Our objective is to minimize the total wasted time of the schedule, that is, the sum of all delays plus the idle times of processors waiting for the last processor to finish. We introduce a new deterministic model for this setting, based on estimated ranges [α(w), β(w)] for processing times of chunks of size w. Depending on α, β, and a measure for the overall deviation from these estimates, we can prove matching upper and lower bounds on the wasted time, the former being achieved by our new balancing strategy. This is in sharp contrast with previous work that, even under the strong assumption of independent, approximately normally distributed chunk processing times, proposed only heuristic scheduling schemes supported merely by empirical evidence. Our model naturally subsumes this stochastic setting, and our generic analysis is valid for most of the existing schemes too, proving them to be non-optimal.

关键词： parallel processing systems

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