Résumé (EN)

We study the Lazy Bureaucrat scheduling problem (Arkin, Bender, Mitchell and Skiena [1]) in the case of common arrivals and deadlines. In this case the goal is to select a subset of given jobs in such a way that the total processing time is minimized and no other job can fit into the schedule. Our contribution comprises a linear time 4/3-approximation algorithm and an FPTAS, which respectively improve on a linear time 2-approximation algorithm and a PTAS given for the more general case of common deadlines [2,3]. We then consider a selfish perspective, in which jobs are submitted by players who may falsely report larger processing times, and show a tight upper bound of 2 on the approximation ratio of strategyproof mechanisms, even randomized ones. We conclude by introducing a maximization version of the problem and a dedicated greedy algorithm.