TY - JOUR

T1 - Envy-free makespan approximation

AU - Cohen, Edith

AU - Feldman, Michal

AU - Fiat, Amos

AU - Kaplan, Haim

AU - Olonetsky, Svetlana

PY - 2012

Y1 - 2012

N2 - We study envy-free mechanisms for assigning tasks to agents, where every task may take a different amount of time to perform by each agent, and the goal is to get all the tasks done as soon as possible (i.e., minimize the makespan). For indivisible tasks, we put forward an envy-free polynomial mechanism that approximates the minimal makespan to within a factor of O(logm), where m is the number of machines. This bound is almost tight, as we also show that no envy-free mechanism can achieve a better bound than Ω(log m/log logm). This improves the recent result of Mu'alem [On multi-dimensional envy-free mechanisms, in Proceedings of the First International Conference on Algorithmic Decision Theory, F. Rossi and A. Tsoukias, eds., Lecture Notes in Comput. Sci. 5783, Springer, Berlin, 2009, pp. 120-131] who introduced the model and gave an upper bound of (m+1)/2 and a lower bound of 2-1/m. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan. Finally, we demonstrate how our mechanism for envy-free makespan minimization can be interpreted as a market clearing problem.

AB - We study envy-free mechanisms for assigning tasks to agents, where every task may take a different amount of time to perform by each agent, and the goal is to get all the tasks done as soon as possible (i.e., minimize the makespan). For indivisible tasks, we put forward an envy-free polynomial mechanism that approximates the minimal makespan to within a factor of O(logm), where m is the number of machines. This bound is almost tight, as we also show that no envy-free mechanism can achieve a better bound than Ω(log m/log logm). This improves the recent result of Mu'alem [On multi-dimensional envy-free mechanisms, in Proceedings of the First International Conference on Algorithmic Decision Theory, F. Rossi and A. Tsoukias, eds., Lecture Notes in Comput. Sci. 5783, Springer, Berlin, 2009, pp. 120-131] who introduced the model and gave an upper bound of (m+1)/2 and a lower bound of 2-1/m. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan. Finally, we demonstrate how our mechanism for envy-free makespan minimization can be interpreted as a market clearing problem.

KW - Algorithmic mechanism design

KW - Envy-free

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=84861635360&partnerID=8YFLogxK

U2 - 10.1137/100801597

DO - 10.1137/100801597

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84861635360

SN - 0097-5397

VL - 41

SP - 12

EP - 25

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 1

ER -