On the competitiveness of scheduling dynamically injected tasks on processes prone to crashes and restarts

Georgiou, Chryssis; Kowalski, Dariusz R.

doi:10.1016/j.jpdc.2015.07.007

Cited by 8 publications

(6 citation statements)

References 32 publications

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“…3.3 for a (single-channel) counterexample. Georgiou and Kowalski (2015) consider the same problem in a distributed setting, distinguishing between different information models. As communication and synchronization pose new challenges, they restrict their attention to jobs of unit size only and no speedup.…”

Section: Multiple Channels or Machinesmentioning

confidence: 99%

On packet scheduling with adversarial jamming and speedup

Böhm

Jeż

Sgall³

et al. 2019

Ann Oper Res

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In Packet Scheduling with Adversarial Jamming, packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these parameters in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of φ + 1 ≈ 2.618 on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1, 4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al.

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Section: Multiple Channels or Machinesmentioning

confidence: 99%

On packet scheduling with adversarial jamming and speedup

Böhm

Jeż

Sgall³

et al. 2019

Ann Oper Res

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“…However, in most related works preemptive scheduling is considered and optimality is shown only for nearly online algorithms (need to know the time of the next job or machine availability). The work of Georgiou and Kowalski [22] was the one that initiated our study. They consider a cooperative computing system of n message-passing processes that are prone to crashes and restarts, and have to collaborate to complete the dynamically injected tasks.…”

Section: Alg Conditionmentioning

confidence: 99%

“…One of their last results, shows that if tasks have different lengths, even under slightly restricted adversarial patterns, competitiveness is not possible. In [4] we introduced the term of speedup, representing resource augmentation, in order to surpass the NP-hardness shown in [22] and achieve competitiveness in terms of pending load. We found the threshold of necessary speedup under which no algorithm can be competitive, and showed that is also sufficient, proposing optimal algorithms that achieve competitiveness.…”

Section: Alg Conditionmentioning

confidence: 99%

Competitive analysis of fundamental scheduling algorithms on a fault-prone machine and the impact of resource augmentation

Anta

Georgiou

Kowalski

et al. 2018

Future Generation Computer Systems

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“…Georgio et al [9] consider the same problem in a distributed setting, distinguishing between different information models. As communication and synchronization pose new challenges, they restrict their attention to jobs of unit size only and no speedup.…”

Section: Multiple Channels or Machinesmentioning

confidence: 99%

On Packet Scheduling with Adversarial Jamming and Speedup

Böhm

Jeż

Sgall

et al. 2018

Approximation and Online Algorithms

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In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes.Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these parameters in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of φ + 1 ≈ 2.618 on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum.Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1,4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. [10] and the lower bound by Anta et al. [1].deviates from previous work, which focused on the case with no speedup or on the speedup sufficient for ratio 1, ignoring intermediate cases. Competitive Analysis and its ExtensionsCompetitive analysis focuses on determining the competitive ratio of an online algorithm. The competitive ratio coincides with the approximation ratio, i.e., the supremum over all valid instances I of OPT(I)/ALG(I), which is the ratio of the optimum profit to the profit of an algorithm ALG on instance I. 1 This name, as opposed to approximation ratio, is used for historical reasons, and stresses that the nature of the hardness at hand is not due to computational complexity, but rather the online mode of computation, i.e., processing an unpredictable sequence of requests, completing each without knowing the future. Note that the optimum solution is to the whole instance, so it can be thought of as being determined by an algorithm that knows the whole instance in advance and has unlimited computational power; for this reason, the optimum solution is sometimes called "offline optimum". Competitive analysis, not yet called this way, was first applied by Sleator and Tarjan to analyze list update and paging problems [19]. Since then, it was employed to the study of many online optimization problems, as evidenced by (now somewhat dated) textbook by Borodin and El-Yaniv [6]. A nice overview of competitive analysis and its many extensions in the scheduling context, including...

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On the competitiveness of scheduling dynamically injected tasks on processes prone to crashes and restarts

Cited by 8 publications

References 32 publications

On packet scheduling with adversarial jamming and speedup

On packet scheduling with adversarial jamming and speedup

Competitive analysis of fundamental scheduling algorithms on a fault-prone machine and the impact of resource augmentation

On Packet Scheduling with Adversarial Jamming and Speedup

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