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 worst-case analysis and approximation schemes of Theoretical Computer Science. For instance, the 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 average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem [Nisan and Ronen 1999]. One version of this problem which includes a verification component is studied by [Koutsoupias 2014]. 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 any independent and identical distribution, the average-case approximation ratio of the mechanism given in [Koutsoupias 2014] 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.

1298-1304

Zhang, Jie

6bad4e75-40e0-4ea3-866d-58c8018b225a

7 February 2018

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 Press.
.

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 worst-case analysis and approximation schemes of Theoretical Computer Science. For instance, the 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 average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem [Nisan and Ronen 1999]. One version of this problem which includes a verification component is studied by [Koutsoupias 2014]. 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 any independent and identical distribution, the average-case approximation ratio of the mechanism given in [Koutsoupias 2014] 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.

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** Average-case Approximation Ratio of Scheduling without Payments
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## More information

Accepted/In Press date: 1 January 2018

e-pub ahead of print date: 7 February 2018

Published date: 7 February 2018

Venue - Dates:
AAAI-18: Thirty-Second AAAI Conference on Artificial Intelligence, Hilton New Orleans Riverside, New Orleans, United States, 2018-02-02 - 2018-02-07

## Identifiers

Local EPrints ID: 418288

URI: http://eprints.soton.ac.uk/id/eprint/418288

PURE UUID: be217792-81e0-44c4-a41a-cc159fa288e5

## Catalogue record

Date deposited: 27 Feb 2018 17:30

Last modified: 16 Mar 2024 06:15

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## Contributors

Author:
Jie Zhang

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