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Efficient parallel exponentiation in GF(2n) using normal basis representations 01

Efficient parallel exponentiation in GF(2n) using normal bas...

引用

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

作者： Lee, M.-K. Kim, Y. Park, K. Cho, Y. School of Computer Science/Eng. Seoul National University Seoul 151-742 Korea Republic of

ISBN: (纸本)9781581134094

Von zur Gathen proposed an efficient parallel exponentiation algorithm in finite fields using normal basis representations. In this paper we present a processor-efficient parallel exponentiation algorithm in GF(2n) which improves upon von zur Gathen's algorithm. We also show that exponentiation in GF(2n) can be done in O(log n) time using n/(log n)2 processors. Hence we get processor × time bound O(n/log n), which is optimal. Finally, we present an on-line processor assignment scheme which was missing in von zur Gathen's algorithm, and show that its time complexity is negligible.

关键词： parallel processing systems

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Approximation algorithms for structured communication problems 97

Approximation algorithms for structured communication proble...

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Proceedings of the 1997 9th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Barth, Dominique Fraigniaud, Pierre Universite de Paris Sud - CNRS Orsay France

ISBN: (纸本)9780897918909

Given a network of processors, a structured communication problem consists to route a communication pattern known in advance. Structured communication problems appear frequently in parallel computing. Hence, communication libraries (e.g, PVM or MPI) generally include a specific access to procedures solving the most common problems of this type. A standard communication model assumes that information proceeds by a sequence of calls between neighboring nodes of the network, and that each node is allowed to call at most one neighbor at a time. In this context, most of the decision problems corresponding to the usual structured communication problems have been shown to be NP-complete. Therefore, several approximation algorithms have been proposed to solve specific problems. Each of these algorithms is dedicated to a particular problem. In this paper, we present a high level method which can be used to derive approximation algorithms for many different structured communication problems on arbitrary networks. This method is shown to be quite efficient. For instance, in the case of broadcasting (one-to-all) and gossiping (all-to-all), it allows to obtain algorithms which approach, and even sometime achieve, the performances of the best known algorithms which were designed using specific techniques defined in purpose for each problem. Moreover, in the case of scattering (personalized one-to-all) and multi-scattering (personalized all-to-all), our method allows to obtain optimal results. Our method is based on the simulation on arbitrary networks of movements of data induced by communication algorithms derived for specific architectures and/or specific communication models. This simulation uses sophisticated embedding and scheduling techniques.

关键词： parallel algorithms

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Using tadpoles to reduce memory and communication requirements for exhaustive, breadth-first search using distributed computers 97

Using tadpoles to reduce memory and communication requiremen...

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Proceedings of the 1997 9th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Cooperman, Gene Tselman, Michael Northeastern Univ Boston MA United States

ISBN: (纸本)9780897918909

A parallel variant of breadth-first search for distributed computing is presented. The variant allows exhaustive enumeration of elements of a search space (implicitly defined graph) in which the representation of all graph nodes would otherwise require more than the total available memory. This algorithm requires the use of a tadpole data structure to partition the search space into connected subgraphs, with each subgraph stored within the memory of a single processor. Thus, the graph of the nodes are stored in a way that adds greater spatial locality, thereby reducing communication among processors. The algorithm enumerates the tadpoles in a breadth-first manner while executing depth-first search within each tadpole. The search within each tadpole is reduced to tree search. A parameter is defined that allows a linear tradeoff in which memory and communication are each reduced linearly as CPU time grows. The result appears to fill a gap in the literature, which has concentrated on parallel depth-first search, but has been relatively sparse in the case of parallel breadth-first search.

关键词： parallel processing systems

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Bounds on the efficiency of message-passing protocols for parallel computers 93

Bounds on the efficiency of message-passing protocols for pa...

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Proceedings of the 5th annual acm symposium on parallel algorithms and architectures

作者： Cypher, Robert Konstantinidou, Smaragda IBM Almaden Research Center San Jose CA

ISBN: (纸本)0897915992

This paper considers the problem of creating message-passing protocols for parallel computers. It is assumed that the processors are connected by a network that provides guaranteed delivery of every message, provided that each message delivered by the network is removed by the receiving processor unconditionally and in finite time. Two models of message-passing are considered, namely a selective model in which the receiver specifies the source of the message, and a nonselective model in which the receiver accepts messages from all sources. We consider only space-efficient protocols in which each processor has storage for a constant number of messages and message headers. We present three main results. First, we give a protocol for the selective model that performs a constant amount of communication per send or receive posted by the application. Second, we prove that no such efficient protocol exists for the nonselective model. Third, we present a protocol for the nonselective model that performs a logarithmic amount of communication per send or receive posted by the application. © 1993 acm.

关键词： Message passing

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

Processor efficient parallel solution of linear systems over...

引用

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 Planar Subgraph Isomorphism and Vertex Connectivity 20

Parallel Planar Subgraph Isomorphism and Vertex Connectivity

引用

32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Gianinazzi, Lukas Hoefler, Torsten Swiss Fed Inst Technol Dept Comp Sci Zurich Switzerland

ISBN: (纸本)9781450369350

We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a near-linear work dependency on the size of the target graph. Existing low depth algorithms do not guarantee that the work remains asymptotically the same for any constant-sized pattern. By using a connection to certain separating cycles, our subgraph isomorphism algorithm can decide the vertex connectivity of a planar graph (with high probability) in asymptotically near-linear work and poly-logarithmic depth. Previously, no sub-quadratic work and poly-logarithmic depth bound was known in planar graphs (in particular for distinguishing between four-connected and five-connected planar graphs).

关键词： graph algorithms parallel algorithms subgraph isomorphism planar graphs vertex connectivity parameterized complexity

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parallel algorithms FOR ARRANGEMENTS 90

PARALLEL ALGORITHMS FOR ARRANGEMENTS

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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： ANDERSON, R BEAME, P BRISSON, E Department of Computer Science and Engineering FR-35 University of Washington Seattle Washington

ISBN: (纸本)0897913701

We give the first efficient parallel algorithms for solving the arrangement problem. We give a deterministic algorithm for the CREW PRAM which runs in nearly optimal bounds of O(log n log n) time and n²/log n processors. We generalize this to obtain an O(log n log n) time algorithm using n^d/log n processors for solving the problem in d dimensions. We also give a randomized algorithm for the EREW PRAM that constructs an arrangement of n lines on-line, in which each insertion is done in optimal O(log n) time using n/log n processors. Our algorithms develop new parallel data structures and new methods for traversing an arrangement.

关键词： Computer programming

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parallel algorithms for finding large cliques in sparse graphs 21

Parallel algorithms for finding large cliques in sparse grap...

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33rd acm symposium on parallelism in algorithms and architectures, SPAA 2021

作者： Gianinazzi, Lukas Besta, Maciej Schaffner, Yannick Hoefler, Torsten ETH Zurich Department of Computer Science Zurich Switzerland ETH Zurich Department of Mathematics Zurich Switzerland

ISBN: (纸本)9781450380706

We present a parallel k-clique listing algorithm with improved work bounds (for the same depth) in sparse graphs with low degeneracy or arboricity. We achieve this by introducing and analyzing a new pruning criterion for a backtracking search. Our algorithm has better asymptotic performance, especially for larger cliques (when k is not constant), where we avoid the straightforwardly exponential runtime growth with respect to the clique size. In particular, for cliques that are a constant factor smaller than the graph's degeneracy, the work improvement is an exponential factor in the clique size compared to previous results. Moreover, we present a low-depth approximation to the community degeneracy (which can be arbitrarily smaller than the degeneracy). This approximation enables a low depth clique listing algorithm whose runtime is parameterized by the community degeneracy. © 2021 acm.

关键词： Approximation algorithms

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Speed Scaling on parallel Processors 07

Speed Scaling on Parallel Processors

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19th annual symposium on parallelism in algorithms and architectures

作者： Albers, Susanne Mueller, Fabian Schmelzer, Swen Univ Freiburg Dept Comp Sci D-79110 Freiburg Germany

ISBN: (纸本)9781595936677

In this paper we investigate algorithmic instruments leading to low power consumption in computing devices. While previous work on energy-efficient algorithms has mostly focused on single processor environments, in this paper we investigate multi-processor settings. We study the basic problem of scheduling a set of jobs, each specified by a release time, a deadline and a processing volume, on variable speed processors so as to minimize the total energy consumption. We first settle the complexity of speed scaling with unit size jobs. More specifically, we devise a polynomial time algorithm for agreeable deadlines and prove NP-hardness results for arbitrary release dates and deadlines. For the latter setting we also develop a polynomial time algorithm achieving a constant factor approximation guarantee that is independent of the number of processors. Additionally, we study speed scaling of jobs with arbitrary processing requirements and, again, develop constant factor approximation algorithms. We finally transform our offline algorithms into constant competitive online strategies.

关键词： multiprocessor scheduling energy efficiency approximation algorithms online algorithms NP-completeness

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