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Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine (or, equivalently, scheduled on some resource).
The activity selection problem is also known as the Interval scheduling maximization problem (ISMP), which is a special type of the more general Interval Scheduling problem. A classic application of this problem is in scheduling a room for multiple competing events, each having its own time requirements (start and end time), and many more arise ...
Uniform machine scheduling (also called uniformly-related machine scheduling or related machine scheduling) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We are given n jobs J 1, J 2, ..., J n of varying processing times, which need to be scheduled on m different machines.
Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of jobs (also called processes or tasks) and a list of machines (also called processors or workers). The required output is a schedule – an assignment of jobs to machines. The schedule should optimize a certain objective ...
The scheduler is an operating system module that selects the next jobs to be admitted into the system and the next process to run. Operating systems may feature up to three distinct scheduler types: a long-term scheduler (also known as an admission scheduler or high-level scheduler), a mid-term or medium-term scheduler, and a short-term scheduler.
The interval scheduling problem can be viewed as a profit maximization problem, where the number of intervals in the mutually compatible subset is the profit. The charging argument can be used to show that the earliest finish time algorithm is optimal for the interval scheduling problem.
Greedy number partitioning (also called the Largest Processing Time in the scheduling literature) loops over the numbers, and puts each number in the set whose current sum is smallest. If the numbers are not sorted, then the runtime is O ( n ) {\displaystyle O(n)} and the approximation ratio is at most 2 − 1 / k {\displaystyle 2-1/k} .
To schedule a job , an algorithm has to choose a machine count and assign j to a starting time and to machines during the time interval [, +,). A usual assumption for this kind of problem is that the total workload of a job, which is defined as d ⋅ p j , d {\displaystyle d\cdot p_{j,d}} , is non-increasing for an increasing number of machines.