Online Scheduling with Hard Deadlines

Goldman, Sally A.; Parwatikar, Jyoti; Suri, Subhash

doi:10.1006/jagm.1999.1060

Cited by 47 publications

(20 citation statements)

References 5 publications

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“…The on-line variant of TCSP is studied in Goldman et al [15) and Goldwasser [16) in the single-machine case. The weight of a job is equal to its length and the algorithms receive the jobs in order of non-decreasing release times.…”

Section: Known Resultsmentioning

confidence: 99%

“…In [15), a deterministic algorithm with ratio 2 if all jobs have the same length and a randomized algorithm with expected ratio O(log c) if the ratio of the longest to the shortest job length is c are presented. Note that "the special case of all jobs having the same length under the arbitrary delay model is of great interest" (quoted from [15)), e.g., for scheduling packets in an ATM switch (where all packets have the same length). In [16), better bounds are derived for the case that the slack of a job is at least proportional to its length.…”

Section: Known Resultsmentioning

confidence: 99%

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Interval selection: Applications, algorithms, and lower bounds

Erlebach

Spieksma

2003

Journal of Algorithms

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Given a set of jobs, each consisting of a number of weighted intervals on the real line, and a positive integer m, we study the problem of selecting a maximum weight subset of the intervals such that at most one interval is selected from each job and, for any point p on the real line, at most m intervals containing p are selected. This problem has applications in molecular biology, caching, PCB assembly, combinatorial auctions, and scheduling. It generalizes the problem of finding a (weighted) maximum independent set in an interval graph.We give a parameterized algorithm GREEDY", that belongs to the class of "myopic" algorithms, which are deterministic algorithms that process the given intervals in order of non-decreasing right endpoint and can either reject or select each interval (rejections are irrevocable). We show that there are values of the parameter a so that GREEDY", produces a 2-approximation in the case of unit weights, an 8-approximation in the case of arbitrary weights, and a (3 + 2V2)-approximation in the case where the weights of all intervals corresponding to the same job are equal. If all intervals have the same length, we prove for m = 1,2 that GREEDY", achieves ratio 6.638 in the case of arbitrary weights and 5 in the case of equal weights per job.Concerning lower bounds, we show that for instances with intervals of arbitrary lengths, no deterministic myopic algorithm can achieve ratio better than 2 in the case of unit weights, better than ~ 7.103 in the case of arbitrary weights, and better than 3 + 2V2 in the case where the weights of all intervals corresponding to the same job are equal. If all intervals have the same length, we give lower bounds of 3 + 2V2 for the case of arbitrary weights and 5 for the case of equal weights per job. Furthermore, we give a lower bound of .:1 ~ 1.582 on the approximation ratio of randomized myopic algorithms in the case of unit weights .• A preliIninary version of some of the results in this paper has appeared in [10].

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Section: Known Resultsmentioning

confidence: 99%

Section: Known Resultsmentioning

confidence: 99%

Interval selection: Applications, algorithms, and lower bounds

Erlebach

Spieksma

2003

Journal of Algorithms

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“…They also present a 2-competitive algorithm for the case of two lengths. These latter results have been generalized by Goldman et al [43], to the case of so-called delays where a delay δ j of an interval j means that if an interval is accepted it must start between s j and s j + δ j .…”

Section: Online Interval Scheduling Problemsmentioning

confidence: 92%

Interval scheduling: A survey

Kolen

Lenstra²,

Papadimitriou

et al. 2007

Naval Research Logistics

193

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Abstract:In interval scheduling, not only the processing times of the jobs but also their starting times are given. This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given "maximal" machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution.

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“…The bound (1 + √ ρ) 2 is optimal as a matching lower bound is given by Baruah et al (1992). There is also a rich literature concerned with non-preemptive scheduling (Lipton & Tomkins, 1994;Goldman, Parwatikar, & Suri, 2000;Goldwasser, 2003;Ding & Zhang, 2006;Ding, Ebenlendr, Sgall, & Zhang, 2007;Ebenlendr & Sgall, 2009). However, it can be easily verified that an algorithm with bounded competitive ratio cannot be designed in the setting of unrestricted values and arbitrary release time.…”

Section: Related Workmentioning

confidence: 99%

“…Therefore, the most common assumption added in the non-preemptive scheduling problem is proportional values, i.e., the value of each job is proportional to the length. In the work of Goldman et al (2000), a tight upper and lower bound of 2 are given for the deterministic competitiveness when all jobs have equal length (thus, equal value), and a 6( log 2 κ + 1)-competitive randomized algorithm is provided for general value of κ, matching the Ω(log κ) lower bound (Lipton & Tomkins, 1994) within a constant factor.…”

Section: Related Workmentioning

confidence: 99%

Efficient Mechanism Design for Online Scheduling

Chen

Liu

et al. 2016

jair

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This paper concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research: one bound is 5, which holds for equal-length jobs; the other bound is κ ln κ + 1 − o(1), which holds for unequal-length jobs, where κ is the maximum ratio between lengths of any two jobs. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for two models: (1) In the preemption-restart model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal ratio of (κ ln κ for unequal-length jobs, where 0 < < 1 is a small constant; (2) In the preemption-resume model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within factor 2) for unequal-length jobs.

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Online Scheduling with Hard Deadlines

Cited by 47 publications

References 5 publications

Interval selection: Applications, algorithms, and lower bounds

Interval selection: Applications, algorithms, and lower bounds

Interval scheduling: A survey

Efficient Mechanism Design for Online Scheduling

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