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More time-work tradeoffs for parallel graph algorithms 91

More time-work tradeoffs for parallel graph algorithms

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

作者： Spencer, Thomas H. Computer Science Department Rensselaer Polytechnic Institute United States

ISBN: (纸本)0897914384

Some parallel algorithms have the property that, as they are allowed to take more time, the total work that they do is reduced. This paper describes three such algorithms that find the strongly connected components of a directed graph. Two of these algorithms are Las Vegas algorithms that run in Õ(t) time and do Õ(n3/t2 + m) and Õ(mn/t + n3/t3) work, respectively. The third is a Monte Carlo algorithm that also runs in O(t) time, but does O (mn + n3/t5) work. The Õ notation means to ignore logarithmic factors. It is also possible to solve the single source shortest path problem with edge lengths between 1 and L in O((n/ρ) log n log(ρL)) time while doing O(nρ 2 log ρ log(ρL)) + Õ(m + n log L) work. Finally, the problem of finding an ear decomposition of a strongly connected directed graph can be reduced to the problem of finding a spanning tree with a. specified root. © 1991 acm.

关键词： Directed graphs

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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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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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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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parallel resource allocation algorithms on macro-pipeline architectures 19

Parallel resource allocation algorithms on macro-pipeline ar...

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19th annual Conference on Computer Science, CSC 1991

作者： Mossaad, Karam M. Wu, Chaun-Lin Computer Science Department South West Texas State University at San Marcos United States Electrical and Computer Engineering Department University of Texas at Austin United States

ISBN: (纸本)0897913825

Resource Allocation is one of the interesting problems in a high speed multiprocess/multiresource environment. In this paper, we present two novel parallel resource allocation algorithms using macro-pipeline architectures. The first algorithm does not allow waiting of processes on resources while the second algorithm does. Both algorithms guarantee the following two properties: high speed and deadlock freedom. The effectiveness of the parallelization approach is studied also via simulation. © 1991 acm.

关键词： Resource allocation

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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

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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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ON FINDING MINIMAL 2-CONNECTED SUBGRAPHS 53

ON FINDING MINIMAL 2-CONNECTED SUBGRAPHS

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2ND annual SYMP OF THE ASSOC FOR COMPUTING MACHINERY AND THE SOC FOR INDUSTRIAL AND APPLIED MATHEMATICS : DISCRETE algorithms

作者： KELSEN, P RAMACHANDRAN, V Department of Computer Sciences University of Texas Austin 78712 TX United States

ISBN: (纸本)0897913760

We present efficient parallel algorithms for the problems of finding a minimal 2-edge-connected spanning subgraph of a 2-edge-connected graph and finding a minimal biconnected spanning subgraph of a biconnected graph. The parallel algorithms for both problems run in polylog time using a linear number of PRAM processors. The problems studied in this paper are of importance in the area of reliable network design. © 1991 Association for Computing Machinery. All rights reserved.

关键词： parallel algorithms

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A SUBLINEAR-TIME RANDOMIZED parallel ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM IN PERFECT GRAPHS 53

A SUBLINEAR-TIME RANDOMIZED PARALLEL ALGORITHM FOR THE MAXIM...

引用

2ND annual SYMP OF THE ASSOC FOR COMPUTING MACHINERY AND THE SOC FOR INDUSTRIAL AND APPLIED MATHEMATICS : DISCRETE algorithms

作者： ALIZADEH, F Computer Science Department University of Minnesota Minneapolis 55455 MN United States

ISBN: (纸本)0897913760

We will show that Lovasz number of graphs may be computed using interior-point methods. This technique will require O(√|V|) iterations, each consisting of matrix operations which have polylog parallel time complexity. In case of perfect graphs Lovasz number equals the size of maximum clique in the graph and thus may be obtained in sublinear parallel time. By using the isolating lemma, we get a Las Vegas randomized parallel algorithm for constructing the maximum clique in perfect graphs. © 1991 Association for Computing Machinery. All rights reserved.

关键词： parallel algorithms

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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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