W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....parts for any task. The longer the optional part executes, the better the quality of the result (the higher the reward) The algorithms proposed for imprecise computation applications concentrate on a model that has an upper bound on the execution time that could be assigned to the optional part [5, 15, 18]. The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally aperiodic scheduling problem of imprecise computation tasks [15, 18] A common assumption in these studies is that the quality of the results produced is a linear function of ....

....on a model that has an upper bound on the execution time that could be assigned to the optional part [5, 15, 18] The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally aperiodic scheduling problem of imprecise computation tasks [15, 18]. A common assumption in these studies is that the quality of the results produced is a linear function of the precision error; consequently, the possibility of having more general error functions is usually not addressed. An alternative model allows tasks to get increasing reward with increasing ....

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....parts for any task. The longer the optional part executes, the better the quality of the result (the higher the reward) The algorithms proposed for imprecise computation applications concentrate on a model that has an upper bound on the execution time that could be assigned to the optional part [7, 21, 27]. The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally the scheduling problem of aperiodic imprecise computation tasks [21, 27] A common assumption in these studies is that the quality of the results produced is a linear ....

....a model that has an upper bound on the execution time that could be assigned to the optional part [7, 21, 27] The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally the scheduling problem of aperiodic imprecise computation tasks [21, 27]. A common assumption in these studies is that the quality of the results produced is a linear function of the precision error; consequently, the possibility of having more general error functions is usually not addressed. An alternative model allows tasks to get increasing reward with increasing ....

[Article contains additional citation context not shown here]

W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....1 Introduction Real time computing models which are able to express the timeliness versus precision trade off are attracting more attention with the advance of applications such as multimedia, image speech processing, information gathering and real time AI. Imprecise Computation (IC) [9, 12], Increased Rewardwith Increased Service (IRIS) 6] and Q RAM [10] models address the problem by logically dividing each task into a mandatory part and an optional part. Despite differences, some This work has been supported by the Defense AdvancedResearch Projects Agency (Contract ....

....by the mandatory part. A non decreasing reward utility function (alternatively, a non increasing error function) is associated with the execution of the optional part to quantify the precision or refinement of the final output. While IC studies have mostly dealt with linear reward functions [9, 12], IRIS [6] and Q RAM [10] models extended the framework to general concave reward functions. Linear and general concave reward functions can successfully represent most of the applications, since most realistic applications (such as multimedia, image processing, real time decision making) exhibit ....

W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....parts for any task. The longer the optional part executes, the better the quality of the result (the higher the reward) The algorithms proposed for imprecise computation applications concentrate on a model that has an upper bound on the execution time that could be assigned to the optional part [5, 15, 18]. The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally aperiodic scheduling problem of imprecise computation tasks [15, 18] A common assumption in these studies is that the quality of the results produced is a linear function of ....

....on a model that has an upper bound on the execution time that could be assigned to the optional part [5, 15, 18] The aim is usually to minimize the (weighted) sum of errors. Several efficient algorithms are proposed to solve optimally aperiodic scheduling problem of imprecise computation tasks [15, 18]. A common assumption in these studies is that the quality of the results produced is a linear function of the precision error; consequently, the possibility of having more general error functions is usually not addressed. An alternative model allows tasks to get increasing reward with increasing ....

[Article contains additional citation context not shown here]

W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

.... The imprecise computation approach is a technique of improving the responsiveness and resource utilization of systems where requirements are less stringent than hard real time envi This work has been supported by the Defense AdvancedResearch Projects Agency (Contract DABT63 96 C 0044) ronments [17, 12]. In this model, every real time task is composed of a mandatory part and an optional part. The mandatory part should be completed by the task s deadline to yield an output of minimal quality. The optional part may be executed after the mandatory part while still before the deadline, if the ....

....that the first derivative of a nondecreasing concave function is nonincreasing. In this paper, we focus on linear and concave reward functions. Maximization of the total reward in a system of tasks with 0 1 constraints, where no reward is accrued for a partial execution was shown to be NP Complete [17]. Continuous convex reward functions results also in an NP Hard problem [2] Although the imprecise computation models allow for greater scheduling flexibility, the timely completion of mandatory parts, even in the presence of faults, is still of utmost importance. A first study incorporating ....

W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....it can avoid timing faults and ensure an acceptable response by discarding some optional tasks. By definition, we say that a real time system is predictable if it can guarantee an acceptable result under all operating conditions. The imprecise computation model used in previous studies [7, 9, 10, 22 26, 31, 38, 39, 41, 49] assumes that the quality of a task s result depends solely on the time spent by the task to produce the result. Specifically, the input of each task is free of error. If a task terminates prematurely, the result produced by it contains an error that is a non decreasing function of the processing ....

....model described in Section 2.1. The ensuing sections examine related work in the areas of error modelling for imprecise computation, anytime algorithms, real time packet scheduling, and congestion control. 2. 1 Imprecise Computation Model The imprecise computation model used in previous studies [7, 9, 10, 22 26, 31, 38, 39, 41, 49] characterizes the workload on a real time system as a set of tasks T = fT 1 ; T 2 ; T q g. A task is a basic unit of work to be scheduled and executed. A task may be a unit of computation, communication, I O, etc. For example, the transmission of a video frame across an ATM network can ....

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....deadlines and provides graceful degradation during a transient overload by ensuring that an approximate result of acceptable quality is available whenever the exact result cannot be obtained in time. The imprecise computation model used in previous studies [3] 4] 5] 6] 7] 8] 9] 10] [11], 12] 13] 14] 15] assumes that the quality of a task s result depends solely on the time spent by the task to produce the result. Specifically, the input of each task is free of error. If a task terminates prematurely, the result produced by it contains an error that is a nondecreasing ....

....result quality of each composite task. Section 6 presents the performance of these algorithms. Lastly, Section 7 summarizes our results and presents future work. 2 BACKGROUND Our model is built on the imprecise computation model used in previous studies [3] 4] 5] 6] 7] 8] 9] 10] [11], 12] 13] 14] 15] which characterizes the workload on a realtime system as a set of preemptable tasks T = T 1 , T 2 , T q . Each task T is logically decomposed into a mandatory part M i followed by an optional part O i and has the following rational parameters: ready time r i . The ....

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W.-K. Shih, J.W.-S. Liu, and J.-Y. Chung, "Algorithms for Scheduling Imprecise Computations to Minimize Total Error," SIAM J. Computing, vol. 20, no. 3, July 1991.

....makes use of Algorithm G described in [15] This optimal off line algorithm finds preemptive schedules of independent tasks in which the maximum fraction of discarded work among all tasks is as small as possible. This algorithm in turn uses the optimal algorithm, developed earlier by Shih et al. [11], for scheduling off line preemptive tasks with arbitrary ready times and deadlines to minimize the sum of the amounts of discarded work over all tasks. While these algorithms allow tasks to be dependent, the possibility of error propagation across dependent tasks was not considered. Shih et al. ....

....reduces to the problem of scheduling a set of independent preemptable tasks. Figure 3 gives a pseudo code description of an algorithm, called S COMPOSITE, for scheduling composite tasks. This algorithm makes use of a modified version of the earliest deadline first algorithm (M EDF) described in [11], and Algorithm G, described in [15] The M EDF algorithm treats every composite task as if it were entirely optional and schedules the composite tasks on an earliest deadline first basis. It never schedules any composite task after its deadline. In other words, every composite task is terminated ....

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

....version of some of the tasks. While the sieve and multiple version methods may be more widely applicable, they are not ideal for two reasons. First, the system must anticipate and decide ahead of time whether to schedule a sieve or primary version. This leads to a higher scheduling overhead [19]. Second, and more importantly, these methods, unlike the milestone method, cannot be easily integrated with traditional fault tolerance methods. For these reasons, we prefer to use the milestone method whenever possible. 3 Scheduling Methods We logically divide each task T i into two parts: a ....

....system to account for the varying degrees that the quality of the results of individual tasks impact the overall quality of the result produced by all the tasks in the system. Examples of optimal and suboptimal algorithms which minimize the total amount of discarded work can be found in [3, 18, 19]. The qualities of results produced by some tasks (e.g. those based on most iterative algorithms and statistical methods) improve faster during the early part of their execution, and the rates of improvement slow as the tasks execute. In this case, the average quality of the results produced by ....

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3):537--552, June 1991.

....makes use of Algorithm G described in [15] This optimal off line algorithm finds preemptive schedules of independent tasks in which the maximum fraction of discarded work among all tasks is as small as possible. This algorithm in turn uses the optimal algorithm, developed earlier by Shih et al. [11], for scheduling off line preemptive tasks with arbitrary ready times and deadlines to minimize the sum of the amounts of discarded work over all tasks. While these algorithms allow tasks to be dependent, the possibility 1 In previous studies on imprecise computation, E i was called the error in ....

....an algorithm, called S COMPOSITE, for scheduling composite tasks. In this figure, we use h j to denote the sum P n j i=1 h j i ; it is the maximum extendedmandatory processing time. This algorithm makes use of a modified version of the earliest deadlinefirst algorithm (M EDF) described in [11], and Algorithm G, described in [15] The M EDF algorithm treats every composite task as if it were entirely optional and schedules the composite tasks on an earliest deadline first basis. It never schedules any composite task after its deadline. In other words, every composite task is terminated ....

[Article contains additional citation context not shown here]

W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

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W.-K. Shih, J. W.-S. Liu, and J.-Y. Chung. Algorithms for scheduling imprecise computations to minimize total error. SIAM Journal on Computing, 20(3), July 1991.

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