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Average-case approximation ratio of scheduling without payments

Average-case approximation ratio of scheduling without payments
Average-case approximation ratio of scheduling without payments
Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the \emph{worst-case analysis} and \emph{approximation schemes} of Theoretical Computer Science. For instance, the \emph{approximation ratio}, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs.

In this paper, we take the \emph{average-case analysis} approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem~\cite{NR99}. One version of this problem which includes a verification component is studied by~\citet{DBLP:journals/mst/Koutsoupias14}. It was shown that the problem has a tight approximation ratio bound of $(n+1)/2$ for the single-task setting, where $n$ is the number of machines. We show, however, when the costs of the machines to executing the task follow \emph{any} independent and identical distribution, the \emph{average-case approximation ratio} of the mechanism given in ~\cite{DBLP:journals/mst/Koutsoupias14} is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio, and indicates that the optimal mechanism for the problem actually works well on average, although in the worst-case the expected cost of the mechanism is $\Theta{(n)}$ times that of the optimal cost.
AAAI
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Zhang, Jie (2018) Average-case approximation ratio of scheduling without payments. In The Thirty-Second AAAI Conference on Artificial Intelligence. AAAI..

Record type: Conference or Workshop Item (Paper)

Abstract

Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the \emph{worst-case analysis} and \emph{approximation schemes} of Theoretical Computer Science. For instance, the \emph{approximation ratio}, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs.

In this paper, we take the \emph{average-case analysis} approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem~\cite{NR99}. One version of this problem which includes a verification component is studied by~\citet{DBLP:journals/mst/Koutsoupias14}. It was shown that the problem has a tight approximation ratio bound of $(n+1)/2$ for the single-task setting, where $n$ is the number of machines. We show, however, when the costs of the machines to executing the task follow \emph{any} independent and identical distribution, the \emph{average-case approximation ratio} of the mechanism given in ~\cite{DBLP:journals/mst/Koutsoupias14} is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio, and indicates that the optimal mechanism for the problem actually works well on average, although in the worst-case the expected cost of the mechanism is $\Theta{(n)}$ times that of the optimal cost.

Text Average-case Approximation Ratio of Scheduling without Payments - Accepted Manuscript
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Accepted/In Press date: 1 January 2018
Published date: 7 February 2018

Identifiers

Local EPrints ID: 418288
URI: https://eprints.soton.ac.uk/id/eprint/418288
PURE UUID: be217792-81e0-44c4-a41a-cc159fa288e5
ORCID for Jie Zhang: ORCID iD orcid.org/0000-0003-1380-9952

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Date deposited: 27 Feb 2018 17:30
Last modified: 07 Jul 2018 04:01

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