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Universal sequencing on an unreliable machine
, 2011
"... We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. Our objective is to minimize ∑ wjf(Cj) for any nondecreasing, ..."
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Cited by 5 (1 self)
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We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. Our objective is to minimize ∑ wjf(Cj) for any nondecreasing, nonnegative, differentiable cost function f(Cj). We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. Our algorithms can be adapted to run in polynomial time with slightly increased cost. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n / log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee.
Universal sequencing on a single machine
, 2010
"... We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion t ..."
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Cited by 5 (4 self)
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We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n / log log n) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee.
ProjectTeam moais Multiprogrammation et Ordonnancement pour les Applications Interactives de Simulation Grenoble RhôneAlpes
"... c t i v it y e p o r t ..."
ProjectTeam moais Multiprogrammation et Ordonnancement pour les Applications Interactives de Simulation Grenoble RhôneAlpes
"... c t i v it y e p o r t ..."