Algorithms for preemptive scheduling of different classes of processors to do jobs with fixed times

Dondeti, V. Reddy; Emmons, Hamilton

doi:10.1016/0377-2217(93)90243-g

Cited by 4 publications

(7 citation statements)

References 12 publications

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“…Papadimitriou [66] proved that ISMA is NP-complete, by a reduction from the circular arc coloring problem; see also [2,10,15,27,32]. In Section 4.1 we show that ISMA and CAC are, in fact, polynomially equivalent.…”

Section: Interval Scheduling With Machine Availabilitiesmentioning

confidence: 86%

“…Finally, preemptive versions of interval scheduling problems are investigated by Bouzina [12], Dondeti and Emmons [27], Kroon et al [57], and Fischetti et al [33]. Notice that with preemption we refer here to interrupting a job, and resuming it immediately on another machine.…”

Section: Online Interval Scheduling Problemsmentioning

confidence: 99%

“…1 and 2). This idea is used in Papadimitriou's proof ( [66]); it also appears in Fischetti et al [32], Biró et al [10], Dondeti and Emmons [27], and Brucker and Nordmann [15]. The reverse operation, that is, viewing the ISMA instance on the time axis, and next connecting the leftmost point and the rightmost point to each other, is used to turn an ISMA instance in a CAC instance.…”

Section: Circular Arc Coloringmentioning

confidence: 99%

“…When the number T of machine types is part of the input, a reduction from CAC, very similar to the one proposed by Papadimitriou [66] for ISMA, shows that HIS(T ) is NPcomplete, even when there is exactly one machine of each type. Dondeti and Emmons [27] establish NP-completeness of HIS(T ) without the latter restriction.…”

Section: Problem: Hierarchical Interval Scheduling With T Machine Typmentioning

confidence: 99%

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Interval scheduling: A survey

Kolen

Lenstra²,

Papadimitriou

et al. 2007

Naval Research Logistics

191

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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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Section: Interval Scheduling With Machine Availabilitiesmentioning

confidence: 86%

Section: Online Interval Scheduling Problemsmentioning

confidence: 99%

Section: Circular Arc Coloringmentioning

confidence: 99%

Section: Problem: Hierarchical Interval Scheduling With T Machine Typmentioning

confidence: 99%

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Interval scheduling: A survey

Kolen

Lenstra²,

Papadimitriou

et al. 2007

Naval Research Logistics

191

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“…Constraints (4) ensure that each train is assigned to exactly one route. Constraints (5) guarantee that only allowed train-route combinations are selected. These constraints may include constraints due to safety considerations, coupling and uncoupling of trains, and service aspects.…”

Section: Formulation As An Integer Programmentioning

confidence: 99%

Routing trains through railway stations: complexity issues

Kroon

Romeijn

Zwaneveld

1997

European Journal of Operational Research

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In this paper we consider the problem of routing trains through railway stations. This problem occurs as a subproblem in the project DONS that is currently being carded out under the supervision of Railned and Netherlands Railways. The project DONS involves the determination of the required future capacity of the Dutch railway infrastructure. In this paper we focus on the computational complexity of the problem of routing trains through railway stations. After an extensive description of the problem, we show that only a subset of the sections and routes of a railway station needs to be taken into account. Then we show that the routing problem is NP-complete as soon as each train has three routing possibilities. However, if each train has only two routing possibilities, then the problem can be solved in an amount of time that is polynomial in the number of trains. Furthermore, if the layout of the railway station is fixed, then the latter is also the case for the problem of finding an assignment of a maximum number of trains to routes that is feasible from a safety point of view. This result can be extended to the case where coupling and uncoupling of trains, certain service considerations, and a cyclic timetable have to be taken into account. (~) 1997 Elsevier Science B.V.

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