Scheduling Parallel Machines On-line
SIAM Journal on Computing
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
How to route and tax selfish unsplittable traffic
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Setting lower bounds on truthfulness: extended abstract
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Truthful algorithms for scheduling selfish tasks on parallel machines
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Truthful approximation mechanisms for scheduling selfish related machines
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Scheduling selfish tasks: about the performance of truthful algorithms
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Improving the price of anarchy for selfish routing via coordination mechanisms
ESA'11 Proceedings of the 19th European conference on Algorithms
Randomized truthful algorithms for scheduling selfish tasks on parallel machines
Theoretical Computer Science
Randomized truthful algorithms for scheduling selfish tasks on parallel machines
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Winner-imposing strategyproof mechanisms for multiple Facility Location games
Theoretical Computer Science
Theory of Computing Systems
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We consider the problem of designing truthful mechanisms for scheduling n tasks on a set of m parallel related machines in order to minimize the makespan. In what follows, we consider that each task is owned by a selfish agent. This is a variant of the KP-model introduced by Koutsoupias and Papadimitriou (Proc. of STACS 1999, pp. 404---413, 1999) (and of the CKN-model of Christodoulou et al. in Proc. of ICALP 2004, pp. 345---357, 2004) in which the agents cannot choose the machine on which their tasks will be executed. This is done by a centralized authority, the scheduler. However, the agents may manipulate the scheduler by providing false information regarding the length of their tasks. We introduce the notion of increasing algorithm and a simple reduction that transforms any increasing algorithm into a truthful one. Furthermore, we show that some of the classical scheduling algorithms are indeed increasing: the LPT algorithm, the PTAS of Graham (SIAM J. Appl. Math. 17(2):416---429, 1969) in the case of two machines, as well as a simple PTAS for the case of m machines, with m a fixed constant. Our results yield a randomized r(1+驴)-approximation algorithm where r is the ratio between the largest and the smallest speed of the related machines. Furthermore, by combining our approach with the classical result of Shmoys et al. (SIAM J. Comput. 24(6):1313---1331, 1995), we obtain a randomized 2r(1+驴)-competitive algorithm. It has to be noticed that these results are obtained without payments, unlike most of the existing works in the field of Mechanism Design. Finally, we show that if payments are allowed then our approach gives a (1+驴)-algorithm for the off-line case with related machines.