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parallel algorithms for routing in non-blocking networks 91

Parallel algorithms for routing in non-blocking networks

引用

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

作者： Lin, Geng Pippenger, Nicholas Department of Computer Science University of British Columbia VancouverBCV6T 1W5 Canada

ISBN: (纸本)0897914384

Non-blocking networks have many applications in communications. Typical examples are telephone switching networks and communication networks among processors or between processors and memory devices. We construct non-blocking networks that are efficient not only as regards their cost and delay, but also as regards the time and space required to control them. In this paper, we present the first simultaneous "weakly optimal" solutions for the explicit construction of non-blocking networks, the design of algorithms and the design of data-structures. "Weakly optimal" is in the sense that all measures of complexity (size and depth of the network, time for the algorithm, and space for the data-structure) are within one or more factors of logn of their smallest possible values. In fact, we explicitly construct a scheme in which networks with n inputs and n outputs have size O(n(logn)2) and depth O(logn). And we present deterministic and randomized on-line parallel algorithms to establish and abolish routes dynamically in these networks. The deterministic algorithm uses O((logn) 5) steps to process any number of transactions in parallel (with one processor per transaction), maintaining a data structure that use O(n(logn) 2) words and the randomized algorithm uses O((logn) 2) expected steps to process any number of transactions in parallel (with one processor per transaction), maintaining a data structure that use O(n(logn) 2) words. © 1991 acm.

关键词： Data structures

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Processor efficient parallel solution of linear systems over an abstract field 91

Processor efficient parallel solution of linear systems over...

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3rd annual acm symposium on parallel algorithms and architectures - SPAA'91

作者： Kaltofen, E. Pan, V. Department of Computer Science Rensselaer Polytechnic Institute Troy New York and Department of Computer Science University of Toronto Toronto Canada M5S 1A4 Department of Mathematics and Computer Science Lehman College City University of New York Bronx New York

parallel randomized algorithms are presented that solve n-dimensional systems of linear equations and compute inverses of n × n non-singular matrices over a field in O((log n)2) time, where each time unit represe... 详细信息

ISBN: (纸本)0897914384

parallel randomized algorithms are presented that solve n-dimensional systems of linear equations and compute inverses of n × n non-singular matrices over a field in O((log n)²) time, where each time unit represents an arithmetic operation in the field generated by the matrix entries. The algorithms utilize within a O(log n) factor as many processors as are needed to multiply two n × n matrices. The algorithms avoid zero divisions with controllably high probability provided the O(n) random elements used are selected uniformly from a sufficiently large set. For fields of small positive characteristic, the processor count measures of our solutions are somewhat higher. © 1991 acm.

关键词： Matrix algebra

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Fast and reliable parallel hashing 91

Fast and reliable parallel hashing

引用

3rd annual acm symposium on parallel algorithms and architectures - SPAA'91

作者： Bast, H. Saarlands, U. Hagerup, T. Fachbereich Informatik Universität des Saarlandes W-6600 Saarbrücken Germany Max-Planck-Institut für Informatik W-6600 Saarbrücken Germany

ISBN: (纸本)0897914384

A perfect hash function for a (multi)set X of n integers is an infective function h : X → {1,., s}, where s = O(n), that can be stored in O(n) space and evaluated in constant time by a single processor. We show that a perfect hash function for a given multiset of n integers can be constructed optimally in O(log∗n) time using O(n/log∗n) processors. Our algorithm is faster than all previously published methods. More significantly, it is highly reliable: Whereas analyses of previous fast parallel hashing schemes provided bounds on the expected resource requirements only, our algorithm is guaranteed to stay within the bounds given with overwhelming probability. © 1991 acm.

关键词： Hash functions

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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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In-place techniques for parallel convex hull algorithms 3

In-place techniques for parallel convex hull algorithms

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

作者： Ghouse, Mujtaba R. Goodrich, Michael T. Dept. of Computer Science Johns Hopkins University BaltimoreMD21218-2686 United States

ISBN: (纸本)0897914384

We present a number of efficient parallel algorithms for constructing 2- and 3-dimensional convex hulls on a randomized CRCW PRAM. Specifically, we show how to build the convex hull of n pre-sorted points in the plane almost surely in O(1) time using O(n log n) processors, or, alternately, almost surely in O (log∗ n) time using an optimal number of processors. We also show how to find the convex hull of n unsorted points in R2 (resp., R3) in O(log2 n) time using O(n log h) work (resp., O(log2n) time using O(min{nlog2 h, n log n}) work), with very high probability, where h is the number of edges in the convex hull (h is O(n), but can be as small as O(l)). Our algorithms for unsorted input depend on the use of new in-place procedures, that is, procedures that are defined on a subset of elements in the input and that work without re-ordering the input. For the pre-sorted case we also exploit a technique that allows one to modify an algorithm that assumes it is given points so that it can be used on hulls;we call such algorithms point-hull invariant. © 1991 acm.

关键词： parallel algorithms

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Large-scale sorting in parallel memories 91

Large-scale sorting in parallel memories

引用

Third annual acm symposium on parallel algorithms and architectures - SPAA'91

作者： Nodine, M.H. Vitter, J.S. Dept. of Computer Science Brown University Providence R. I.

ISBN: (纸本)0897914384

We present several algorithms for sorting efficiently with parallel two-level and multilevel memories. Our main result is an elegant, easy-to-implement, optimal, deterministic algorithm for external sorting with P disk drives. This result answers the open problem posed by Vitter and Shriver. Our measure of performance is the number of parallel input/output (I/O) operations, in which each of the P disks can simultaneously transfer a block of B contiguous records. Our optimal algorithm is deterministic, and thus it improves upon the optimal randomized algorithm of [ViS] as well as the well-known deterministic but nonoptimal technique of disk striping. The second part of the paper broadens our coverage from two-level memories to more general multilevel memories. In particular we consider the blocked uniform memory hierarchy (UMH) introduced by Alpern, Carter, and Feig, and its parallelization P-UMH, along with new variants. We give optimal and nearly-optimal algorithms for a wide range of bandwidth degradations, including a parsimonious algorithm for constant bandwidth. We also develop optimal sorting algorithms for all bandwidths for other versions of UMH and P-UMH, including natural restrictions we introduce called RUMH and P-RUMH, which more closely correspond to current programming languages. © 1991 acm.

关键词： Bandwidth

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Balanced routing. Towards the distance bound on grids 91

Balanced routing. Towards the distance bound on grids

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3rd annual acm symposium on parallel algorithms and architectures - SPAA'91

作者： Kunde, M. Institut f. Informatik TU Munich Arcisstr. 21 D-8000 Munich 2 Germany

The problem of packet routing on an r-dimensional mesh-connected array or grid of processors with side-length n is studied. Each processor is able to store rf(n) packets, f(n) 1-1/r. The new class of balanced routing ... 详细信息

ISBN: (纸本)0897914384

The problem of packet routing on an r-dimensional mesh-connected array or grid of processors with side-length n is studied. Each processor is able to store rf(n) packets, f(n) < n^1-1/r. The new class of balanced routing problems is introduced which includes such fundamental problems as partial h - h routing. On 3-dimensional n × n × n grids (without wrap-arounds) partial permutation problems and so-called (1, f(n))-balanced problems can be solved by a deterministic routing algorithm needing only 3.333n + O(n/f(n)^1/2) steps which is asymptotically only 11.11 percent larger than the distance bound of 3n - 3 steps. The result is better than those of so far known randomized algorithms, routing data only with high probability. The new algorithm also beats previous deterministic routing algorithms. For arbitrary r, r > 3, permutation routing on r-dimensional cubes can be performed in asymptotically (2r - 3+l/r)n steps which again is faster than the running times of so far known algorithms, both randomized and deterministic ones. A further improvement leads to an algorithm with approximately (r + (r - 2)(I/r)^1/(r-2))n + O(n/f(n) ^1/(r-1)) transport steps. For a constant buffer size of O((r²/ϵ) ^r-1) packets, ϵ > 0, a number of (r+(r - 2)(l/r) ^1/(r-2)/ + ϵ)n steps can be achieved. The number of steps is reduced to the half if the algorithms are adapted to tori of processors, i.e. grids with wrap-around connections. Furthermore, algorithms for the general h - h routing problem are presented which also needs a smaller number of steps than previous algorithms. It is shown that these problems can be solved in O((h + r)n) instead of O(hrn) needed before. © 1991 acm.

关键词： parallel algorithms

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

SPAA '90 Proceedings of the 2nd Annual ACM Symposium on Para...

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

This conference proceeding contains 45 papers. The topics covered include: routing algorithms;array processing;message passing;fault tolerance;hypercubes;scheduling;parallel algorithms;memory sharing;computational com... 详细信息

ISBN: (纸本)0897913701

关键词： Computer Programming

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ASYNCHRONOUS SHARED MEMORY parallel COMPUTATION - (PRELIMINARY VERSION) 90

ASYNCHRONOUS SHARED MEMORY PARALLEL COMPUTATION - (PRELIMINA...

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2ND annual SYMP OF THE ASSOC FOR COMPUTING MACHINERY : parallel algorithms AND architectures ( SPAA 90 ) / AEGEAN WORKSHOP ON COMPUTING

作者： NISHIMURA, N University of Toronto

ISBN: (纸本)0897913701

The contributions of this paper are twofold. First, we outline criteria by which any model of asynchronous shared memory parallel computation can be judged. Previous models are considered with respect to these factors. Next, we introduce a new model, and show that this model fulfils all the listed requirements. We also analyze in our model the complexity of several fundamental parallel algorithms.

关键词： Computer systems, Digital

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Generalized sweep methods for parallel computational geometry 90

Generalized sweep methods for parallel computational geometr...

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

作者： Goodrich, Michael T. Ghouse, Mujtaba R. Bright, Jonathan Johns Hopkins Univ Baltimore MD United States

ISBN: (纸本)0897913701

In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using generalized versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include general hidden-surface elimination (even if the overlap relation contains cycles), CSG boundary evaluation, computing the contour of a collection of rectangles, and hidden-surface elimination for rectangles. Our algorithms are for the CREW PRAM.

关键词： Computer programming

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