Minimizing Makespan for the Lazy Bureaucrat Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
The Lazy Bureaucrat scheduling problem
Information and Computation
Asymptotic fully polynomial approximation schemes for variants of open-end bin packing
Information Processing Letters
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
On lazy bin covering and packing problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Improved approximation algorithms for maximum resource bin packing and lazy bin covering problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Hardness of lazy packing and covering
Operations Research Letters
Scheduling selfish tasks: about the performance of truthful algorithms
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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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.