Characterizing sets of jobs that admit optimal greedy-like algorithms

The “ Priority Algorithm” is a model of computation introduced by Borodin, Nielsen and Rackoff [BNR03] which formulates a wide class of greedy algorithms. For an arbitrary set S of jobs, we are interested in whether or not there exists a priority algorithm that gains optimal profit on every subset of S. In the case where the jobs are all intervals, we characterize such sets S and give an efficient algorithm (when S is finite) for determining this. We show that in general, however, the problem is NP-hard.