Week 1 - Scheduling.docx

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Computer Science
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Anna Bretscher

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Interval Scheduling Problem Aim: Schedule the jobs so that the number of jobs scheduled is maximized and jobs do not overlap Notation: J: The set of jobs th i: The i job s: The start time of the i job i th fi The finish time of the i job Algorithm: Ordering: Sort the jobs by increasing finish time. 3 ,6j 1 j7, j4, 2 ,5j , j Scheduling: Schedule each job if there are no conflicts. j3, 7 ,5j Proof if the algorithm is best - Proof by Contradiction: Idea: Play Devil’s Advocate Assume our solution is not the best. This means there is a better solution B Show that our algorithm’s solution is as good as B by making B equivalent
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