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Superlinear Performance In RealTime Parallel Computation
 Journal of Supercomputing
, 2001
"... Can a parallel computer with n processors solve a computational problem more than n times faster than a sequential computer? Can it solve it more than n times better? New computational paradigms offer an affirmative answer to the above questions through concrete examples in which the improvement i ..."
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Cited by 28 (18 self)
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Can a parallel computer with n processors solve a computational problem more than n times faster than a sequential computer? Can it solve it more than n times better? New computational paradigms offer an affirmative answer to the above questions through concrete examples in which the improvement in speed or quality is superlinear in the number of processors used by the parallel computer. Furthermore, the improvement is consistent and provable. All examples are characterized by the presence of one or several realtime input streams. In one of the examples, an exponential improvement in speed is achieved despite the fact that the processors of the parallel computer are significantly slower than their sequential counterpart. In another example, the improvement in quality is unbounded. A metaphor from everyday life motivates each computational paradigm in which a superlinear improvement in performance is exhibited. Key words and phrases: Parallelism, superlinear speedup, superlinear qualityup, realtime computation, optimization, cryptography, numerical analysis. 1
Parallel RealTime Optimization: Beyond Speedup
 PARALLEL PROCESSING LETTERS
, 1999
"... Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? ..."
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Cited by 25 (23 self)
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Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for realtime optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the bestpossible approximation to the minimumweight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimumweight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained seque...
Parallel RealTime Computation: Sometimes Quantity Means Quality
 Computing and Informatics
, 2000
"... The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. Th ..."
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Cited by 14 (13 self)
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The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. The thesis of this paper is that a second equally important motivation for using parallel computers exists. Specifically, the following question is posed: Can parallel computers, thanks to their multiple processors, do more than simply speed up the solution to a problem? We show that within the paradigm of realtime computation, some classes of problems have the property that a solution to a problem in the class, when computed in parallel, is far superior in quality than the best one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, `better' means `closer to optimal' for optimization problems, `more secure' for crypto...
Parallel RealTime Numerical Computation: Beyond Speedup III
 International Journal of Computers and their Applications, Special Issue on High Performance Computing Systems
"... Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime ..."
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Cited by 14 (13 self)
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Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime paradigm. In this setting, numerical data required to solve a problem are received as input by a computer system, at regular intervals. The computer must process its inputs as soon as they arrive. It must also produce its outputs at regular intervals, as soon as they are available. We show that for some realtime numerical problems a parallel computer can deliver a solution that is significantly more accurate than when computed by a sequential computer. Similar results were derived recently in the areas of realtime optimization and realtime cryptography. Key words and phrases: Parallelism, realtime computation, numerical analysis. This research was supported by the Natural Sciences a...
Secure File Transfer: A Computational Analog to the Furniture Moving Paradigm
 PARALLEL AND DISTRIBUTED COMPUTING PRACTICES
, 1999
"... One of the most compelling illustrations of the power of parallelism is the furnituremoving paradigm. In it, a large item of furniture needs to be moved from one place to another. A single mover, working alone, must take the item apart, move each piece separately, and then reassemble the item a ..."
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Cited by 9 (8 self)
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One of the most compelling illustrations of the power of parallelism is the furnituremoving paradigm. In it, a large item of furniture needs to be moved from one place to another. A single mover, working alone, must take the item apart, move each piece separately, and then reassemble the item at the new location, taking a long time to complete the job. By contrast, four movers can simply lift the item and quickly move it to its new location. Thus, the time required to accomplish the task is reduced by a factor significantly larger than four. This paper describes a computational analog to the furnituremoving paradigm. The computation in question is concerned with transferring a computer file from one computer system to another over an insecure communications channel. The file contains private or sensitive information whose secrecy and integrity need to be maintained. Cryptography is used to obtain a digital signature of the file, thereby protecting its integrity, and the...
Parallel RealTime Cryptography: Beyond Speedup II
 II, PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON PARALLEL AND DISTRIBUTED PROCESSING TECHNIQUES AND APPLICATIONS, LAS VEGAS
, 2000
"... The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. However, it was shown recently that a second equally important motivation for using parallel computers exists: Within the paradigm of realtime computation, some cl ..."
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Cited by 8 (8 self)
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The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. However, it was shown recently that a second equally important motivation for using parallel computers exists: Within the paradigm of realtime computation, some classes of problems have the property that a solution to a problem in the class computed in parallel is better than the one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, for optimization problems, `better' means `closer to optimal'. The present paper continues this line of inquiry by exploring another class enjoying the aforementioned property, namely, cryptographic problems in a realtime setting. In this class, `better' means `more secure'. A realtime cryptographic problem is presented for which the parallel solution is significantly better than a sequential one.
Discrete Steepest Descent In Real Time
 Parallel and Distributed Computing Practices
, 2001
"... A general framework is proposed for the study of realtime algorithms. The framework unifies previous algorithmic definitions of realtime computation. In it, state space traversal is used as a model for computational problems in a realtime environment. The proposed framework also employs a paradig ..."
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Cited by 6 (4 self)
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A general framework is proposed for the study of realtime algorithms. The framework unifies previous algorithmic definitions of realtime computation. In it, state space traversal is used as a model for computational problems in a realtime environment. The proposed framework also employs a paradigm, known as discrete steepest descent, for algorithms designed to solve these problems. Sequential and parallel algorithms for traversing a state space by discrete steepest descent are then analyzed and compared. The analysis measures the value (or worth) of a computed solution. The quantity used in the evaluation may be the time required by an algorithm to reach the solution, the quality of the solution obtained, or any similar measure. The value of a realtime solution obtained in parallel is shown to be consistently superior to that of a solution computed sequentially by an amount superlinear in the size of the problem.
Nonlinearity, Maximization, and Parallel RealTime Computation
 Proceedings of the 12th Conference on Parallel and Distributed Computing and Systems, Las Vegas
, 2000
"... This paper focuses on the improvement in the quality of computation provided by parallelism. The problem of interest is that of computing the maximum of a nonlinear feedback function in a realtime environment. We show that the solution obtained in parallel is asymptotically better than that comp ..."
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Cited by 4 (4 self)
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This paper focuses on the improvement in the quality of computation provided by parallelism. The problem of interest is that of computing the maximum of a nonlinear feedback function in a realtime environment. We show that the solution obtained in parallel is asymptotically better than that computed sequentially. Key words and phrases: Parallelism, realtime computation, nonlinear feedback function, maximization. This research was supported by the Natural Sciences and Engineering Research Council of Canada. 1 1 Introduction The central motivation behind parallelism has always been the speeding up of sequential computations. Recently, another aspect of parallel computation was brought to light. It was shown that under some circumstances it is possible to obtain in parallel solutions to computational problems that are significantly better than any solutions computed sequentially. This phenomenon was demonstrated, in a realtime environment, for problems in combinatorial optimiz...
Parallel RealTime Complexity Theory
, 2002
"... We present a new complexity theoretic approach to realtime computations. We define timed ωlanguages as a new formal model for such computations, that we believe to allow a unified treatment of all variants of realtime computations that are meaningful in practice. To our knowledge, such a practic ..."
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Cited by 2 (0 self)
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We present a new complexity theoretic approach to realtime computations. We define timed ωlanguages as a new formal model for such computations, that we believe to allow a unified treatment of all variants of realtime computations that are meaningful in practice. To our knowledge, such a practically meaningful formal definition does not exist at this time. In order to support our claim that timed ωlanguages capture all the realtime characteristics that are important in practice, we use this formalism to model the two most important features of realtime algorithms, namely the presence of deadlines and the realtime arrival of input data. We emphasize the expressive power of our model by using it to formalize aspects from the areas of realtime database systems and ad hoc networks. We also offer a complexity theoretic characterization of parallel realtime computations. First, we define complexity classes that capture the intuitive notion of resource requirements for realtime computations in a parallel environment. Then, we show that realtime algorithms form an infinite hierarchy with respect to the number of processors used, and
On limits on the computational power of dataaccumulating algorithms
 Information Processing Letters
"... In the dataaccumulating paradigm, inputs arrive continuously in real time, and the computation terminates when all the already received data are processed before another datum arrives. Previous research states that a constant upper bound on the running time of a successful algorithm within this par ..."
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Cited by 2 (2 self)
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In the dataaccumulating paradigm, inputs arrive continuously in real time, and the computation terminates when all the already received data are processed before another datum arrives. Previous research states that a constant upper bound on the running time of a successful algorithm within this paradigm exists only for particular forms of the data arrival law. This contradicts our recent conjecture that those problems that are solvable in real time are included in the class of logarithmic spacebounded computations. However, we prove that such an upper bound does exist in fact in both the parallel and sequential cases and for any polynomial arrival law, thus strengthening the mentioned conjecture. Then, we analyze an example of a noncontinuous data arrival law. We find similar properties for the sorting algorithm under such a law, namely the existence of an upper bound on the running time, suggesting that such properties do not depend on the form of the arrival law.