Interval scheduling: A survey

Kolen, Antoon; Lenstra, Jan Karel; Papadimitriou, Christos H.; Spieksma, Frits

doi:10.1002/nav.20231

Cited by 193 publications

(89 citation statements)

References 70 publications

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“…Within the broad range of interval scheduling results (see the survey papers by Kolen et al (2007) and Kovalyov et al (2007)), those relevant to our study deal with identical parallel machines or uniform machines. In the case of identical parallel machines, the fastest algorithms for minimizing the job rejection cost have time complexity O(n log n) if all jobs have equal weights (Carlisle and Lloyd 1995) and O(mn log n) if job weights are allowed to be different (Bouzina and Emmons 1996); the fastest algorithm for minimizing the machine usage cost is of time complexity O(n log n) if machine weights are equal (Gupta et al 1979).…”

Section: Related Workmentioning

confidence: 99%

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Shioura

Shakhlevich

Strusevich

et al. 2017

J Sched

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We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(n log n) time in the singlemachine case and in O(n 2 m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution.

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Section: Related Workmentioning

confidence: 99%

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Shioura

Shakhlevich

Strusevich

et al. 2017

J Sched

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“…Interval graphs naturally occur in many scheduling applications [5,19]. In a unit interval graph, all representing intervals are open and have the same length, while in a trivially perfect graph, any two representing intervals are either disjoint or one is properly contained in the other.…”

Section: Interval Graphsmentioning

confidence: 99%

Partitioning Perfect Graphs into Stars

Bevern

Bredereck

Bulteau

et al. 2016

Journal of Graph Theory

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The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NPcomplete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvable cases, for example, on interval graphs and bipartite permutation graphs, and also NP-complete cases, for example, on grid graphs and chordal graphs.

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“…Similarly to the previous scheme, when a regular policy is applied, the time interval between two consecutive services is set to a xed value whereas in a exible policy, the time interval between two consecutive executions of a service is restricted within a minimum and/or maximum limit (e.g. Kolen et al, 2007). …”

Section: Problems With Recurrent Servicesmentioning

confidence: 99%

Scheduling policies for multi-period services

Nunez-del-Toro

Fernández

Kalcsics

et al. 2016

European Journal of Operational Research

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This paper discusses a multi-period service scheduling problem. In this problem, a set of customers is given who periodically require service over a finite time horizon. To satisfy the service demands, a set of operators is given, each with a fixed capacity in terms of the number of customers an operator can serve per period. The task is to determine for each customer the periods in which he will be visited by an operator such that the periodic service requests of the customers are adhered to and the total number of operators used over the time horizon is minimal. Two alternative policies for scheduling customer visits are considered. In the first one, a customer is visited just on time, i.e., in the period where he or she has a demand for service. The second policy allows service visits ahead of time. The rationale behind this policy is that allowing irregular visits may reduce the overall number of operators needed throughout the time horizon. To solve the problem, integer linear programming formulations are proposed for both policies and numerical experiments are presented that show the reduction in the number of operators used when visits ahead of time are allowed. As only small instances can be solved optimally, a heuristic algorithm is introduced in order to obtain good quality solutions and shorter computing times.Peer ReviewedPostprint (author's final draft

show abstract

Interval scheduling: A survey

Cited by 193 publications

References 70 publications

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Partitioning Perfect Graphs into Stars

Scheduling policies for multi-period services

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