Common Deadline Lazy Bureaucrat Scheduling Revisited

Abstract

Lazy bureaucrat scheduling is a new class of scheduling problems introduced by Arkin et al. [1]. 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. [2]. 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 [2]. 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 function [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.

Research supported by NSFC grant No. 10231060 and No. 60573020.