Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
A simplified NP-complete MAXSAT problem
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
Interval selection: applications, algorithms, and lower bounds
Journal of Algorithms
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Maximizing Weighted number of Just-in-Time Jobs on Unrelated Parallel Machines
Journal of Scheduling
On the complexity of scheduling tasks with discrete starting times
Operations Research Letters
Open problems in throughput scheduling
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We study an offline interval scheduling problem where every job has exactly one associated interval on every machine. To schedule a set of jobs, exactly one of the intervals associated with each job must be selected, and the intervals selected on the same machine must not intersect. We show that deciding whether all jobs can be scheduled is NP-complete already in various simple cases. In particular, by showing the NP-completeness for the case when all the intervals associated with the same job end at the same point in time (also known as just-in-time jobs), we solve an open problem posed by Sung and Vlach (J. Sched., 2005). We also study the related problem of maximizing the number of scheduled jobs. We prove that the problem is NP-hard even for two machines and unit-length intervals. We present a 2/3-approximation algorithm for two machines (and intervals of arbitrary lengths).