On lazy bureaucrat scheduling with common deadlines

Abstract

Lazy bureaucrat scheduling is a new class of scheduling problems introduced by Arkin et al. (Inf. Comput. 184:129–146, 2003). In this paper we focus on the case where all the jobs share a common deadline. Such a problem is denoted as CD-LBSP, which has been considered by Esfahbod et al. (Algorithms and data structures. Lecture notes in computer science, vol. 2748, pp. 59–66, 2003). We first show that the worst-case ratio of the algorithm SJF (Shortest Job First) is two under the objective function [min-time-spent], and thus answer an open question posed in (Esfahbod, et al. in Algorithms and data structures. Lecture notes in computer science, vol. 2748, pp. 59–66, 2003). We further present two approximation schemes A _k and B _k both having worst-case ratio of $\frac{k+1}{k}$ , for any given integer k>0, under the objective functions [min-makespan] and [min-time-spent], respectively. Finally, we prove that the problem CD-LBSP remains NP-hard under several objective functions, even if all jobs share the same release time.