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Buttercup has given Westley a set of tasks t...,, to complete on the farm. Each task t, - (d ) is associated with a deadline

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Buttercup has given Westley a set of tasks t...,, to complete on the farm. Each task t, - (d ) is associated with a deadline d; and an estimated amount of time w needed to complete the task. To express his undying love to Buttercup, Westley strives to complete all the assigned tasks as early as possible. However, some deadlines might be a bit too demanding, so it may not be possible for him to finish a task by its deadline; some tasks may need extra time and therefore will be completed late. Your goal (inconceivable!) is to help Westley minimize the deadline overruns of any task; if he starts task t, at time, he will finish at time s+w. The deadline overrun (or lateness) of tasks denoted L-fort, is the value L i -diiffi >d; otherwise Give a polynomial-time algorithm that computes the optimal order T for Westley to complete Buttercup's tasks so as to minimize the maximum L across all tasks. That is, your algorithm should compute T that minimizes min max L TI In other words, you do not want Westley to complete any task too late, so you minimize the deadline overrun of the task completed that is most past its deadline. Prove that your algorithm produces an optimal schedule and analyze its running time, Buttercup has given Westley a set of tasks t...,, to complete on the farm. Each task t, - (d ) is associated with a deadline d; and an estimated amount of time w needed to complete the task. To express his undying love to Buttercup, Westley strives to complete all the assigned tasks as early as possible. However, some deadlines might be a bit too demanding, so it may not be possible for him to finish a task by its deadline; some tasks may need extra time and therefore will be completed late. Your goal (inconceivable!) is to help Westley minimize the deadline overruns of any task; if he starts task t, at time, he will finish at time s+w. The deadline overrun (or lateness) of tasks denoted L-fort, is the value L i -diiffi >d; otherwise Give a polynomial-time algorithm that computes the optimal order T for Westley to complete Buttercup's tasks so as to minimize the maximum L across all tasks. That is, your algorithm should compute T that minimizes min max L TI In other words, you do not want Westley to complete any task too late, so you minimize the deadline overrun of the task completed that is most past its deadline. Prove that your algorithm produces an optimal schedule and analyze its running time

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