Problem 1:

Consider the scheduling problem. Assume the goal is to reduce the sum of the lateness of requests. Demonstrate that for this objective function, the earliest-deadline-first algorithm doesn’t always find out an optimal schedule.

Problem 2:

Consider the scheduling problem. Assume every request has the positive weight Wi and the goal is to reduce the weighted sums of lateness. Provide an efficient algorithm for special case that all deadlines are equivalent to the time the resource becomes available.

Remember that when the problem asks you to design the algorithm, you should also prove the algorithm's correctness and examine its running time. The running time should be bounded by the polynomial function of input size.