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An important class of scheduling algorithms is the class of dynamic priority algorithms. When none of the intervals overlap the optimum solution is trivial. The optimum for the non-weighted version can found with the earliest deadline first scheduling. Weighted interval scheduling is a generalization where a value is assigned to each executed ...
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 ...
The algorithm has several stages. First, find a solution using greedy algorithm. In each iteration of the greedy algorithm the tentative solution is added the set which contains the maximum residual weight of elements divided by the residual cost of these elements along with the residual cost of the set.
Longest-processing-time-first (LPT) is a greedy algorithm for job scheduling. The input to the algorithm is a set of jobs, each of which has a specific processing-time. There is also a number m specifying the number of machines that can process the jobs. The LPT algorithm works as follows:
The modified due date scheduling is a scheduling heuristic created in 1982 by Baker and Bertrand, [1] used to solve the NP-hard single machine total-weighted tardiness problem. This problem is centered around reducing the global tardiness of a list of tasks which are characterized by their processing time, due date and weight by re-ordering them.
This algorithm may yield a non-optimal solution. For example, suppose there are two tasks and two agents with costs as follows: Alice: Task 1 = 1, Task 2 = 2. George: Task 1 = 5, Task 2 = 8. The greedy algorithm would assign Task 1 to Alice and Task 2 to George, for a total cost of 9; but the reverse assignment has a total cost of 7.
This optimization algorithm may be used to characterize matroids: if a family F of sets, closed under taking subsets, has the property that, no matter how the sets are weighted, the greedy algorithm finds a maximum-weight set in the family, then F must be the family of independent sets of a matroid. [3]
interval order: Each job has an interval [s x,e x) and job is a predecessor of if and only if the end of the interval of is strictly less than the start of the interval for .= In the presence of a precedence relation one might in addition assume time lags. The time lag between two jobs is the amount of time that must be waited after the first ...