## A Case Study in Real-Time Parallel Computation: Correcting Algorithms (2001)

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Venue: | Journal of Parallel and Distributed Computing |

Citations: | 21 - 19 self |

### BibTeX

@ARTICLE{Bruda01acase,

author = {Stefan D. Bruda and Selim G. Akl},

title = {A Case Study in Real-Time Parallel Computation: Correcting Algorithms},

journal = {Journal of Parallel and Distributed Computing},

year = {2001},

volume = {61},

pages = {688--708}

}

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### Abstract

A correcting algorithm is one that receives an endless stream of corrections to its initial input data and terminates when all the corrections received have been taken into account. We give a characterization of correcting algorithms based on the theory of data-accumulating algorithms. In particular, it is shown that any correcting algorithm exhibits superunitary behavior in a parallel computation setting if and only if the static counterpart of that correcting algorithm manifests a strictly superunitary speedup. Since both classes of correcting and data-accumulating algorithms are included in the more general class of real-time algorithms, we show in fact that many problems from this class manifest superunitary behavior. Moreover, we give an example of a real-time parallel computation that pertains to neither of the two classes studied (namely, correcting and data-accumulating algorithms), but still manifests superunitary behavior. Because of the aforementioned results, the usual measures of performance for parallel algorithms (that is, speedup and efficiency) lose much of their ability to convey effectively the nature of the phenomenon taking place in the real-time case. We propose therefore a more expressive measure that captures all the relevant parameters of the computation. Our proposal is made in terms of a graphical representation. We state as an open problem the investigation of such a measure, including nding an analytical form for it.

### Citations

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Citation Context ...p theorem, states that when two or more processors are applied to solve a given computational problem, the decrease in running time is at most proportional to the increase in the number of processors =-=[4, 13]-=-. Since, according to this result, the ratio of the speedup achieved to the number of processors used is at most 1, the behavior of any parallel algorithm is at most unitary. By contrast, if a paralle... |

54 | On the computational complexity of dynamic graph problems
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Citation Context ...aw such that a correction occurs before the algorithm in question hassnished processing the initial input data. Note that algorithms that correct themselves when their input changes have been studied =-=[10, 11]-=-, but they do not fall within the theory of c-algorithms, since this theory assumes a real{time component, namely the corrections arrival law. We will call such algorithms, where the corrections arriv... |

28 |
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Citation Context ..., a third parameter must be considered, namely the arrival rate, which can substantially aect the performance. Therefore, we propose a new graphical representation. Such a representation was used in [=-=3]-=-, but in another context (that is, to represent time, information, and energy, as originally proposed in [14]). The diagram we propose is a triangle ABC, as insgure 1. On the edge AB the time increase... |

23 |
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(Show Context)
Citation Context ...p theorem, states that when two or more processors are applied to solve a given computational problem, the decrease in running time is at most proportional to the increase in the number of processors =-=[4, 13]-=-. Since, according to this result, the ratio of the speedup achieved to the number of processors used is at most 1, the behavior of any parallel algorithm is at most unitary. By contrast, if a paralle... |

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19 |
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(Show Context)
Citation Context ...nsidered from the point of view of the parallel computation in [1, 2], where it is shown that such constraints can lead to superunitary behavior. The study of the second class of constraints began in =-=[8]-=-, where the class of data{accumulating algorithms (or d-algorithms for short) is introduced. In this paradigm, data that arrive during the computation are considered as an endless stream, the algorith... |

18 | On the data-accumulating paradigm
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(Show Context)
Citation Context ...a that arrive during the computation are considered as an endless stream, the algorithm terminating when all the currently arrived data have been processed. The study of d-algorithms was continued in =-=[5, 6, 9]-=-, where it is shown that such an algorithm manifests superunitary behavior if and only if the parallel speedup for the static case is strictly larger than 1. Moreover, an interesting link between real... |

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(Show Context)
Citation Context ...a that arrive during the computation are considered as an endless stream, the algorithm terminating when all the currently arrived data have been processed. The study of d-algorithms was continued in =-=[5, 6, 9]-=-, where it is shown that such an algorithm manifests superunitary behavior if and only if the parallel speedup for the static case is strictly larger than 1. Moreover, an interesting link between real... |

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2 |
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Citation Context ...r than rebuilding the solution from scratch. Note that one practical case in which the theory of c-algorithms may prove very useful is the emerging area of mobile computing and heterogeneous networks =-=[12, 15]-=-, where the current methods for dealing with mobile hosts when routing packets (e.g. tunneling [15]) may lead to congestion. Therefore, an alternative solution is to compute the routing tables on thes... |

1 |
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Citation Context ...ce. Therefore, we propose a new graphical representation. Such a representation was used in [3], but in another context (that is, to represent time, information, and energy, as originally proposed in =-=[14]-=-). The diagram we propose is a triangle ABC, as insgure 1. On the edge AB the time increases from m t to M t , on the edge CB the arrival rate increases from m r to M r , and the number of processors ... |

1 |
On the Computational Complexity of Dynamic
- Ramalingam, Reps
- 1996
(Show Context)
Citation Context ... such that a correction occurs before the algorithm in question has finished processing the initial input data. Note that algorithms that correct themselves when their input changes have been studied =-=[9, 10]-=-, but they do not fall within the theory of c-algorithms, since this theory assumes a real--time component, namely the corrections arrival law. We will call such algorithms, where the corrections arri... |