Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
Fixed job scheduling with two types of processors
Operations Research - Supplement
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Optimal Solution for the Channel-Assignment Problem
IEEE Transactions on Computers
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Resource allocation with time intervals
Theoretical Computer Science
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We consider a scheduling problem where jobs have to be carried out by parallel identical machines. The attributes of a job j are: a fixed start time s"j, a fixed finish time f"j, and a resource requirement r"j. Every machine owns R units of a renewable resource necessary to carry out jobs. A machine can process more than one job at a time, provided the resource consumption does not exceed R. The jobs must be processed in a non-preemptive way. Within this setting, the problem is to decide whether a feasible schedule for all jobs exists or not. We discuss such a decision problem and prove that it is strongly NP-complete even when the number of resources are fixed to any value R=2. Moreover, we suggest an implicit enumeration algorithm which has O(nlogn) time complexity in the number n of jobs when the number m of machines and the number R of resources per machine are fixed. The role of storage layout and preemption are also discussed.