Abstract
In this work we give a tight lower bound on makespan approximation for envy-free allocation mechanisms dedicated to scheduling tasks on unrelated machines. Specifically, we show that no mechanism exists that can guarantee an envy-free allocation of jobs to m machines with a makespan less than a factor of O(logm) of the minimal makespan. Combined with previous results, this paper definitively proves that the optimal algorithm for obtaining a minimal makespan for any envy-free division can at best approximate the makespan to a factor of O(logm).
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References
Barbanel, J.B.: The Geometry of Efficient Fair Division. Cambridge University Press, Cambridge (2005)
Brams, S.J., Taylor, A.D.: Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge University Press, Cambridge (1996)
Brams, S.J., Taylor, A.D.: The Win-Win Solution: Guaranteeing Fair Shares to Everybody. Norton Paperback, New York (2000)
Cohen, E., Feldman, M., Fiat, A., Kaplan, H., Olonetsky, S.: Envy-Free Makespan Approximation. SIAM J. Comput. 41, 12–25 (2012)
Dubins, L., Spanier, E.: How to Cut a Cake Fairly. American Mathematical Monthly 68, 1–17 (1961)
Foley, D.: Resource Allocation and the Public Sector. Yale Economic Essays 7, 45–98 (1967)
Haake, C.J., Raith, M.G., Su, F.E.: Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair-Division Problems. Social Choice and Welfare 19, 723–749 (2002)
Hartline, J., Leong, S., Mualem, H., Schapira, M., Zohar, A.: Multi-Dimensional Envy-Free Scheduling Mechanisms. Technical Report 1144. The Hebrew University (2008)
Hougaard, J.L.: An Introduction to Allocation Rules. Springer, New York (2009)
Lenstra, J.K., Shmoys, D.B., Tardos, É.: Approximation Algorithms for Scheduling Unrelated Parallel Machines. Mathematical Programming 46, 259–271 (1990)
Meertens, M.: Games, Economies and Fair Allocations: A study in the field of Game Theory. VDM Verlag, Saarbrücken (2009)
Moulin, H.: Fair Division and Collective Welfare. MIT, Cambridge (2003)
Steinhaus, H.: The Problem of Fair Division. Econometrica 16, 101–104 (1948)
Steinhaus, H.: Mathematical Snapshots. Oxford University Press, New York (1951)
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Fiat, A., Levavi, A. (2012). Tight Lower Bounds on Envy-Free Makespan Approximation. In: Goldberg, P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35311-6_46
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DOI: https://doi.org/10.1007/978-3-642-35311-6_46
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