Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A resource-allocation queueing fairness measure
Proceedings of the joint international conference on Measurement and modeling of computer systems
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity
Proceedings of the 8th ACM conference on Electronic commerce
Setting lower bounds on truthfulness: extended abstract
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal envy-free pricing with metric substitutability
Proceedings of the 9th ACM conference on Electronic commerce
Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Uniform Budgets and the Envy-Free Pricing Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A Characterization of 2-Player Mechanisms for Scheduling
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An optimal lower bound for anonymous scheduling mechanisms
Proceedings of the 10th ACM conference on Electronic commerce
Combination Can Be Hard: Approximability of the Unique Coverage Problem
SIAM Journal on Computing
On Multi-dimensional Envy-Free Mechanisms
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Envy-Free Allocations for Budgeted Bidders
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Dynamic pricing for impatient bidders
ACM Transactions on Algorithms (TALG)
Mechanism design for fractional scheduling on unrelated machines
ACM Transactions on Algorithms (TALG)
A lower bound of 1 + ϕ for truthful scheduling mechanisms
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Tight lower bounds on envy-free makespan approximation
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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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 $O(\log m)$, 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 $\Omega(\log m / \log\log m)$. 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.