Preemptive Scheduling of Uniform Processor Systems

Gonzalez, Teofilo F.; Sahni, Sartaj

doi:10.1145/322047.322055

Cited by 195 publications

(106 citation statements)

References 6 publications

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“…Those continuity intervals generalize the concept of the DPSs (Disjoint Processor Systems) of [6,12]. The lemma states that the initial situation where machine weight prefixes dominate job weight prefixes, while the total sum of machine weights equals the total sum of job weights, as described in Proposition 2.4, is preserved in all rounds.…”

Section: Lemma 37 If In Round Iψmentioning

confidence: 89%

“…In Section 4.1 we revisit the makespan problem and we show that the minimal value of our mathematical program when f = max agrees with the makespan of optimal preemptive schedules as derived in [6,12]. In Section 4.2 we apply our analysis to the p -norm,…”

Section: Introductionmentioning

confidence: 87%

“…This case was studied in [11,10,6,12]. Liu and Yang [11] introduced bounds on the cost of optimal schedules.…”

Section: Introductionmentioning

confidence: 99%

“…Horvath, Lam and Sethi proved that the optimal cost is indeed the maximum of those bounds by constructing an algorithm that uses a large number of preemptions. Gonzalez and Sahni [6] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m−1). This number of preemptions was shown to be optimal in the sense that there exist inputs for which every optimal schedule involves that many preemptions.…”

Section: Introductionmentioning

confidence: 99%

“…This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [6] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m − 1). We extend their ideas for general symmetric, convex and monotone target functions.…”

mentioning

confidence: 99%

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Optimal Preemptive Scheduling for General Target Functions

Epstein

Tassa

2004

Lecture Notes in Computer Science

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We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m ≤ n uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target function of the loads on each machine is minimized. This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [6] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m − 1). We extend their ideas for general symmetric, convex and monotone target functions. This general approach enables us to distill the underlying principles on which the optimal makespan algorithm is based. More specifically, the general approach enables us to identify between the optimal scheduling problem and a corresponding problem of mathematical programming. This, in turn, allows us to devise a single algorithm that is suitable for a wide array of target functions, where the only difference between one target function and another is manifested through the corresponding mathematical programming problem.

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Section: Lemma 37 If In Round Iψmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 87%

“…This case was studied in [11,10,6,12]. Liu and Yang [11] introduced bounds on the cost of optimal schedules.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Optimal Preemptive Scheduling for General Target Functions

Epstein

Tassa

2004

Lecture Notes in Computer Science

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Scheduling chains on uniform processors with communication delays

Kubiak¹,

Penz²,

Trystram³

2002

J. Sched.

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SUMMARYWe show that the problem of scheduling chains of unit execution time (UET) jobs on uniform processors with communication delays to minimize makespan is NP-hard in the strong sense. We also give a heuristic that generates solutions with known, and relatively small, absolute error for this problem. The NP-hardness result holds even for the case without communication delays, and complements the earlier result of Gonzalez and Sahni who gave a polynomial time algorithm for preemptive jobs of arbitrary length.We also study the structure of optimal solutions for the two processor problem of scheduling chains of UET jobs with communication delays, where one processor is a (integer) times faster than the other. This investigation leads to a linear time optimization algorithm for this case.

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New applications of the Muntz and Coffman algorithm

Drozdowski

2001

J. Sched.

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SUMMARYMuntz and Co man proposed an algorithm to solve the problem of scheduling preemptable tasks either with arbitrary precedences on two processors, or tasks with tree-like precedences on an arbitrary number of processors, for the schedule length criterion. In this work, we demonstrate that this well-known algorithm has interesting features which extend its application to many other scheduling problems. Three deterministic scheduling problems for preemptable tasks are considered. Though these problems have diverse formulations, they have at least one thing in common: Basically their optimization algorithms boil down to the Muntz-Co man algorithm. The foundations of the Muntz-Co man algorithm versatility are established.

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Preemptive Scheduling of Uniform Processor Systems

Cited by 195 publications

References 6 publications

Optimal Preemptive Scheduling for General Target Functions

Optimal Preemptive Scheduling for General Target Functions

Scheduling chains on uniform processors with communication delays

New applications of the Muntz and Coffman algorithm

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