Common Deadline Lazy Bureaucrat Scheduling Revisited

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 Ak and Bk both having worst-case ratio of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{k+1}{k}$\end{document}, 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.