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15
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 29 (19 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 27 (25 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 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 16 (15 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...
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 15 (14 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...
The Maximum Flow Problem: A RealTime Approach
 Proceedings of the Thirteenth Conference on Parallel and Distributed Computing and Systems
, 2001
"... The dynamic version of the maximum flow problem allows the graph underlying the flow network to change over time. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is modified. These corrections arrive in real time. In this paper, parallel a ..."
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Cited by 11 (5 self)
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The dynamic version of the maximum flow problem allows the graph underlying the flow network to change over time. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is modified. These corrections arrive in real time. In this paper, parallel and sequential solutions to the realtime maximum flow problem are developed on the Reconfigurable Multiple Bus Machine (RMBM) model and on the Random Access Machine (RAM) model, respectively. The parallel solution successfully meets the deadlines imposed in real time, while the sequential one fails to do so. The two solutions are then applied to a realtime process scheduler, an extension of Stone's static twoprocessor allocation problem. The scheduler allows processes to be created and destroyed, the amount of communication between two processes to change with time, and so on. The parallel algorithm is always able to compute the optimal schedule, while the solution obtained sequentially is only an approximation. The improvement provided by the parallel approach over the sequential one is superlinear in the number of processors used by the parallel model. Key words and phrases: maximum flow, parallelism, realtime computation, module allocation. 1
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...
On the Necessity of Formal Models for RealTime Parallel Computations
 3, June & September 2001
, 2000
"... We assume the multitape realtime Turing machine as a formal model for parallel realtime computation. Then, we show that, for any positive integer k, there is at least one language L k which is accepted by a ktape realtime Turing machine, but cannot be accepted by a (k1)tape realtime Turing ma ..."
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Cited by 9 (9 self)
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We assume the multitape realtime Turing machine as a formal model for parallel realtime computation. Then, we show that, for any positive integer k, there is at least one language L k which is accepted by a ktape realtime Turing machine, but cannot be accepted by a (k1)tape realtime Turing machine. It follows therefore that the languages accepted by realtime Turing machines form an infinite hierarchy with respect to the number of tapes used. Although this result was previously obtained in [1], our proof is considerably shorter, and explicitly builds the languages L k .
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 9 (9 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.
RealTime Minimum Vertex Cover For TwoTerminal SeriesParallel Graphs
 Proceedings of the Thirteenth Conference on Parallel and Distributed Computing and Systems
, 2000
"... Tree contraction is a powerful technique for solving a large number of graph problems on families of recursively definable graphs. The method is based on processing the parse tree associated with a member of such a family of graphs in a bottomup fashion, such that the solution to the problem is ..."
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Cited by 8 (8 self)
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Tree contraction is a powerful technique for solving a large number of graph problems on families of recursively definable graphs. The method is based on processing the parse tree associated with a member of such a family of graphs in a bottomup fashion, such that the solution to the problem is obtained at the root of the tree. Sequentially, this can be done in linear time with respect to the size of the input graph. In parallel, efficient and even cost optimal tree contraction algorithms have also been developed. In this paper we show how the method can be applied to compute the cardinality of the minimum vertex cover of a twoterminal seriesparallel graph. We then construct a realtime paradigm for this problem and show that in the new computational environment, a parallel algorithm is superior to the best possible sequential algorithm, in terms of the accuracy of the solution computed. Specifically, there are cases in which the solution produced by a parallel algorithm ...
Pursuit and Evasion on a Ring: An Infinite Hierarchy for Parallel RealTime Systems
, 2001
"... We present a new complexity theoretic approach to realtime parallel computations. Based on the theory of timed omegalanguages, we define complexity classes that capture the intuitive notion of resource requirements for realtime computations in a parallel environment. Then, we show that, for any p ..."
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Cited by 7 (7 self)
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We present a new complexity theoretic approach to realtime parallel computations. Based on the theory of timed omegalanguages, we define complexity classes that capture the intuitive notion of resource requirements for realtime computations in a parallel environment. Then, we show that, for any positive integer n, there exists at least one timed omegalanguage Ln which is accepted by a 2nprocessor realtime algorithm using arbitrarily slow processors, but cannot be accepted by a (2n1)processor realtime algorithm. It follows therefore that realtime algorithms form an infinite hierarchy with respect to the number of processors used. Furthermore, such a result holds for any model of parallel computation.