23.4. Interval Scheduling Problem

Try these first

1. 1.

   Explain the goals of the Interval Scheduling Problem.

   Hint

   Think about the challenges of overlapping requests.

2. 2.

   What is a greedy algorithm in this context?

   Hint

   Focus on the selection criteria.

3. 3.

   What strategy does the greedy algorithm employ in the Interval Scheduling Problem?

   • Maximizing total weight
   • Choosing the earliest finish time
   • Random selection

   Hint

   Remember the main goal of a greedy approach.

4. 4.

   True or False: In the case of weighted requests, the greedy strategy remains optimal.

   • True
   • False

   Hint

   Consider how weight impacts choices.

5. 5.

   Given a set of bookings with different weights: (1,5,3), (2,6,6), and (3,7,4), implement a dynamic programming solution to find the maximum weight schedule.

   Hint

   Create a matrix that records the best possible weight for each interval choice.

6. 6.

   Design a greedy solution for a weighted variation of interval scheduling that still attempts to ensure maximum weight; explain the limitations of this approach.

   Hint

   Consider edge cases where a high-weight booking conflicts with a series of smaller weight bookings.