TY - GEN

T1 - Makespan Minimization via Posted Prices

AU - Feldman, Michal

AU - Fiat, Amos

AU - Roytman, Alan

N1 - Publisher Copyright:
© 2017 ACM.

PY - 2017/6/20

Y1 - 2017/6/20

N2 - We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: The ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm.We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.

AB - We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: The ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm.We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.

KW - Job scheduling

KW - Load balancing

KW - Makespan

KW - Pricing schemes

UR - http://www.scopus.com/inward/record.url?scp=85025828982&partnerID=8YFLogxK

U2 - 10.1145/3033274.3085129

DO - 10.1145/3033274.3085129

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AN - SCOPUS:85025828982

T3 - EC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation

SP - 405

EP - 422

BT - EC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

T2 - 18th ACM Conference on Economics and Computation, EC 2017

Y2 - 26 June 2017 through 30 June 2017

ER -