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The anarchy of scheduling without money

Giannakopoulos, Yiannis and Koutsoupias, Elias and Kyropoulou, Maria (2016) The anarchy of scheduling without money. In: Algorithmic Game Theory 9th International Symposium, SAGT 2016, 2016-09-19 - 2016-09-21, Liverpool, UK.

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Abstract

We consider the scheduling problem on n strategic unrelated machines when no payments are allowed, under the objective of minimizing the makespan. We adopt the model introduced in [Koutsoupias 2014] where a machine is bound by her declarations in the sense that if she is assigned a particular job then she will have to execute it for an amount of time at least equal to the one she reported, even if her private, true processing capabilities are actually faster. We provide a (non-truthful) randomized algorithm whose pure Price of Anarchy is arbitrarily close to 1 for the case of a single task and close to n if it is applied independently to schedule many tasks, which is asymptotically optimal for the natural class of anonymous, task-independent algorithms. Previous work considers the constraint of truthfulness and proves a tight approximation ratio of (n+1)/2 for one task which generalizes to n(n+1)/2 for many tasks. Furthermore, we revisit the truthfulness case and reduce the latter approximation ratio for many tasks down to n, asymptotically matching the best known lower bound. This is done via a detour to the relaxed, fractional version of the problem, for which we are also able to provide an optimal approximation ratio of 1. Finally, we mention that all our algorithms achieve optimal ratios of 1 for the social welfare objective.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published proceedings: Theoretical Computer Science
Uncontrolled Keywords: Mechanism design without payments; Price of anarchy; Scheduling unrelated machines; Approximation algorithms
Divisions: Faculty of Science and Health
Faculty of Science and Health > Computer Science and Electronic Engineering, School of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 24 Mar 2022 18:28
Last Modified: 24 Mar 2022 18:28
URI: http://repository.essex.ac.uk/id/eprint/23652

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