Exploring the Optimality Proof of Earliest Finish Time Algorithm

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In summary, the conversation discusses the optimality proof of the earliest finish time algorithm and the confusion about the terms "solution still feasible" and "optimal." The proof assumes that the greedy algorithm matches the optimal solution up to a certain point but not beyond, and explains that this contradicts the definition of r. The conversation also mentions a diagram showing that the r+1th job finishes at the same time for both greedy and optimal, which further supports the contradiction.
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Homework Statement


I am trying to understand the optimality proof of the earliest finish time algorithm. I have attached the pdf which I am reading. It's just 2 pages. I don't understand what they mean with solution still feasible and optimal (but contradicts maximality of r). An explanation from scratch would be nice...

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The proof supposes that the greedy algorithm matches the optimal solution, in regard to job finish times, up to and including the first r jobs, but not the first r+1. Clearly, if greedy is not optimal, there must be such an r, 0<=r<n. Note that optimal here just means that the finish time of the nth job is as early as it could be.
In the second diagram, the r+1th job finishes at the same time in both greedy and optimal. That contradicts the definition of r, since it was defined to be such that greedy was not as good as optimal at the r+1th job.
 

Related to Exploring the Optimality Proof of Earliest Finish Time Algorithm

1. What is the Earliest Finish Time Algorithm?

The Earliest Finish Time (EFT) Algorithm is a scheduling method used to determine the optimal order in which tasks or activities should be completed in order to minimize the total completion time.

2. How does the EFT Algorithm work?

The EFT Algorithm works by assigning a priority to each task or activity based on its earliest finish time. The task with the earliest finish time is given the highest priority and is scheduled to be completed first. This process is repeated until all tasks have been scheduled.

3. What is the optimality proof of the EFT Algorithm?

The optimality proof of the EFT Algorithm states that this scheduling method will always result in the shortest possible completion time for a given set of tasks. This means that there is no other schedule that can be created using the EFT Algorithm that will result in a shorter completion time.

4. What are the benefits of using the EFT Algorithm?

The EFT Algorithm can help to improve efficiency and productivity by ensuring that tasks are completed in the most optimal order. It can also help to reduce the total completion time and minimize the risk of delays or missed deadlines.

5. Are there any limitations to the EFT Algorithm?

While the EFT Algorithm is considered to be a highly effective scheduling method, it does have some limitations. For example, it assumes that all tasks can be completed simultaneously and that there are no resource constraints. Additionally, it may not be suitable for complex projects with a large number of interdependent tasks.

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