Minimum Max-Lateness Job
Scheduling: Inversion Removal
Alternate Schedule with Multiple Inversions:
One such schedule could be: Job 4, Job 1, Job 3, and Job 2.
This schedule clearly doesn't follow the earliest-deadline-first strategy, and contains the
following inversions:
- Job 4 is processed before all other jobs.
- Job 3 is processed before Job 2.
Step-by-Step Removal of Inversions:
Step 1: Move Job 4 to the end, as its deadline is the last among all jobs.
Resultant Schedule: Job 1, Job 3, Job 2, and Job 4.
Step 2: Address the inversion between Job 3 and Job 2 by switching their positions.
Resultant Schedule: Job 1, Job 2, Job 3, and Job 4.
Now, the schedule adheres to the earliest-deadline-first strategy.
Conclusion:
Starting with a schedule containing multiple inversions (Job 4, Job 1, Job 3, and Job 2), we
systematically removed each inversion to arrive at the optimal earliest-deadline-first
schedule (Job 1, Job 2, Job 3, and Job 4).