Common Deadline Lazy Bureaucrat Scheduling Revisited

The Lazy Matroid Problem

“…In fact, Lazy Matroid is a generalization of Lazy Bureaucrat with common arrivals and deadlines, which was shown to admit an FPTAS in [2]; note that in the common arrivals case the two most studied objectives, namely makespan and time-spent coincide. The (weak) NP-hardness of this case was shown by Gai and Zhang [7,3].…”

“…She has a certain budget that she can spend on these projects and she wants to select projects in such a way that as much money as possible are saved (remain unused), yet not enough for any left-out project. This is in fact a 'reincarnation' of the Lazy Bureaucrat Problem [1][2][3][4][5] in which a lazy worker wants to select a set of tasks of minimum total duration in such a way that his remaining working time does not suffice to add any task. Assume further that the Minister has to deal with additional constraints, e.g.…”

“…Earlier results on Lazy Bureaucrat include approximations for the common deadline case: first a tight 2-approximation algorithm working under both objectives was given by Esfahbod, Ghodsi and Sharifi [8] and later two PTAS 's, one for each objective, were presented in [7,3].…”