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Communication Lower Bounds for DistributedMemory Matrix Multiplication
, 2004
"... this paper. More speci cally, we use the de nitions of [10]: (g(n)) is the set of functions f(n) such that there exist positive constants c 1 , c2 , and n0 such that 0 c1 g(n) f(n) c2 g(n) for all n n0 ; O(g(n)) is de ned similarly using the weaker condition 0 f(n) c 2 g(n); g(n)) is de ..."
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Cited by 46 (1 self)
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this paper. More speci cally, we use the de nitions of [10]: (g(n)) is the set of functions f(n) such that there exist positive constants c 1 , c2 , and n0 such that 0 c1 g(n) f(n) c2 g(n) for all n n0 ; O(g(n)) is de ned similarly using the weaker condition 0 f(n) c 2 g(n); g(n)) is de ned with the condition 0 c 1 g(n) f(n). The set o(g(n)) consists of functions f(n) such that for any c 2 > 0 there exists a constant n0 > 0 such that 0 f(n) c 2 g(n) for all n n0
The Design and Analysis of BulkSynchronous Parallel Algorithms
, 1998
"... The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles sharedmemory s ..."
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Cited by 10 (1 self)
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The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles sharedmemory style programming with efficient exploitation of data locality. The BSPRAM model can be optimally simulated by a BSP computer for a broad range of algorithms possessing certain characteristic properties: obliviousness, slackness, granularity. We use BSPRAM to design BSP algorithms for problems from three large, partially overlapping domains: combinatorial computation, dense matrix computation, graph computation. Some of the presented algorithms are adapted from known BSP algorithms (butterfly dag computation, cube dag computation, matrix multiplication). Other algorithms are obtained by application of established nonBSP techniques (sorting, randomised list contraction, Gaussian elimination without pivoting and with column pivoting, algebraic path computation), or use original techniques specific to the BSP model (deterministic list contraction, Gaussian elimination with nested block pivoting, communicationefficient multiplication of Boolean matrices, synchronisationefficient shortest paths computation). The asymptotic BSP cost of each algorithm is established, along with its BSPRAM characteristics. We conclude by outlining some directions for future research.
Numerical Representations as HigherOrder Nested Datatypes
, 1998
"... Number systems serve admirably as templates for container types: a container object of size n is modelled after the representation of the number n and operations on container objects are modelled after their numbertheoretic counterparts. Binomial queues are probably the first data structure that wa ..."
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Cited by 5 (2 self)
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Number systems serve admirably as templates for container types: a container object of size n is modelled after the representation of the number n and operations on container objects are modelled after their numbertheoretic counterparts. Binomial queues are probably the first data structure that was designed with this analogy in mind. In this paper we show how to express these socalled numerical representations as higherorder nested datatypes. A nested datatype allows to capture the structural invariants of a numerical representation, so that the violation of an invariant can be detected at compiletime. We develop a programming method which allows to adapt algorithms to the new representation in a mostly straightforward manner. The framework is employed to implement three different container types: binary randomaccess lists, binomial queues, and 23 finger search trees. The latter data structure, which is treated in some depth, can be seen as the main innovation from a datastruct...
Options for Future Colliders at CERN
, 1998
"... We discuss options for future colliders at CERN# after the LHC# which should address the burning problems of particle physics# mass# #avour and uni#cation. We give and comment upon parameter lists for linear e # e # colliders# # # # # colliders and future larger hadron col# liders that a ..."
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Cited by 5 (3 self)
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We discuss options for future colliders at CERN# after the LHC# which should address the burning problems of particle physics# mass# #avour and uni#cation. We give and comment upon parameter lists for linear e # e # colliders# # # # # colliders and future larger hadron col# liders that are being studied in various places. We discuss how particle physics experiments can be carried out at these colliders. We make a number of observations how these colliders might be constructed on or near to the CERN site# and how the existing expertise and infra#structure might best be employed for their study. Finally# we formulate recommendations for action at CERN. Geneva# Switzerland January 23# 1998 Contents 1 INTRODUCTION 3 2 POST#LHC SCENARIO 4 3 COLLIDERS 6 3.1 Linear e # e # Colliders . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Linear e # e # Collider Parameters . . . . . . . . . . . . . . . 6 3.1.2 Linear e # e # Collider Schedules . . . . . . . . ....
OutputSensitive Methods for Rectilinear Hidden Surface Removal
, 1993
"... We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these t ..."
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Cited by 4 (0 self)
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We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these two components, in that its running time is O(r(n 1 1=r k)), where 1 r log n is a tunable parameter. By using this method while adjusting the parameter r "on the fly" one can achieve a running time that is O(n log n k(log n= log(1 k=n))). Note that when k is \Theta(n), this achieves an O(n log n) running time, and when k is \Theta(n 1 ffl ) for any positive constant ffl, then this achieves an O(k) running time, both of which are optimal. A preliminary announcement of this research is to appear at the 17th International Colloquium on Automata, Languages, and Programming. Part of this research was carried out while the authors were visiting Princeton University for the DIMACS ...
Generic Operations on Nested Datatypes
, 2001
"... Nested datatypes are a generalisation of the class of regular datatypes, which includes familiar datatypes like trees and lists. They typically represent constraints on the values of regular datatypes and are therefore used to minimise the scope for programmer error. ..."
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Cited by 4 (0 self)
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Nested datatypes are a generalisation of the class of regular datatypes, which includes familiar datatypes like trees and lists. They typically represent constraints on the values of regular datatypes and are therefore used to minimise the scope for programmer error.
Bulksynchronous parallel multiplication of Boolean matrices
"... The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. We study the BSP complexity of subcubic algorithms for Boolean matrix multiplication. The communication cost of a standard Strassentype algorithm is known to be optimal for genera ..."
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Cited by 2 (1 self)
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The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. We study the BSP complexity of subcubic algorithms for Boolean matrix multiplication. The communication cost of a standard Strassentype algorithm is known to be optimal for general matrices. A natural question is whether it remains optimal when the problem is restricted to Boolean matrices. We give a negative answer to this question, by showing how to achieve a lower asymptotic communication cost for Boolean matrix multiplication. The proof uses a deep result from extremal graph theory, known as Szemer'edi's Regularity Lemma. Despite its theoretical interest, the algorithm is not practical, because it works only on astronomically large matrices and involves huge constant factors.
Modular Monadic Semantics
"... Modular monadic semantics is a highlevel and modular form of denotational semantics. It is capable of capturing individual programming language features as small building blocks which can be combined to form a programming language of arbitrary complexity. Interactions between features are isolated ..."
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Modular monadic semantics is a highlevel and modular form of denotational semantics. It is capable of capturing individual programming language features as small building blocks which can be combined to form a programming language of arbitrary complexity. Interactions between features are isolated in such a way that the building blocks are invariant. This paper explores the theory and application of modular monadic semantics, including the building blocks for individual programming language features, equational reasoning with laws and axioms, modular proofs, program transformation, modular interpreters, and semanticsdirected compilation. We demonstrate that modular monadic semantics makes programming languages easier to specify, reason about, and implement than the alternative of using conventional denotational semantics. Our contributions include: (a) the design of a fully modular interpreter based on monad transformers, including important features missing from several earlier efforts, (b) a method to lift monad operations through monad transformers, including difficult cases not achieved in earlier work, (c) a study of the semantic implications of the order of monad transformer composition, (d) a formal theory of modular monadic semantics that justifies our choice of liftings based on a notion of naturality, and (e) an implementation of our interpreter in Gofer, whose constructor classes provide just the added power over Haskell type classes to allow precise and convenient expression of our ideas. A note to reviewers: this paper is rather long. Short of resorting to “Part I / Part II”, the one way we see to shorten it would be to remove Section 4 and its Appendix B, which would amount to eliminating contribution (e) above. This would shorten the paper by about 12 pages.
J. Ellis E. Keil G. Rolandi
"... We discuss options for future colliders at CERN# after the LHC# which should address the burning problems of particle physics# mass# #avour and uni#cation. We give and comment upon parameter lists for linear e # e # colliders# # # # # colliders and future larger hadron col# liders that a ..."
Abstract
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We discuss options for future colliders at CERN# after the LHC# which should address the burning problems of particle physics# mass# #avour and uni#cation. We give and comment upon parameter lists for linear e # e # colliders# # # # # colliders and future larger hadron col# liders that are being studied in various places. We discuss how particle physics experiments can be carried out at these colliders. We make a number of observations how these colliders might be constructed on or near to the CERN site# and how the existing expertise and infra#structure might best be employed for their study. Finally# we formulate recommendations for action at CERN. Geneva# Switzerland January 23# 1998 Contents 1