MPI-INF D1 Publications: Journal Article: Maximizing the minimum load: The cost of selfishness

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Author, Editor(s)

Author(s):

Chen, Xujin
Epstein, Leah
Kleiman, Elena
van Stee, Rob

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Not MPG Author(s):

Chen, Xujin
Epstein, Leah
Kleiman, Elena

BibTeX cite key*:

ChEpKS13

Title

Title*:

Maximizing the minimum load: The cost of selfishness

Journal

Journal Title*:	Theoretical Computer Science	Journal's URL:
Download URL for the article:		Language:	English

Publisher

Publisher's Name:	Elsevier	Publisher's URL:	http://www.journals.elsevier.com/theoretical-computer-science/
Publisher's Address:		ISSN:	0304-3975

Vol, No, pp, Date

Volume*:	482	Number:
Publishing Date:	April 2013
Pages*:	9-19	Number of VG Pages:	11
Page Start:		Page End:
Sequence Number:		DOI:

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(LaTeX) Abstract:	We consider a scheduling problem where each job is controlled by a selfish agent, who is only interested in minimizing its own cost, defined as the total load of the machine that its job is assigned to. We consider the objective of maximizing the minimum load (the value of the cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game theoretic context, this problem has not been considered in this setting before. We study the price of anarchy (\poa) and the price of stability (\pos). These measures are unbounded already for two uniformly related machines \cite{EpKS10}, and therefore we focus on identical machines. We show that the $\pos$ is 1, and derive tight bounds on the pure $\poa$ for $m\leq 7$ and on the overall pure $\poa$, showing that its value is exactly 1.7. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, we show that the mixed $\poa$ grows exponentially with $m$ for this problem. In addition, we consider a similar setting of selfish jobs with a different objective of minimizing the maximum ratio between the loads of any pair of machines in the schedule. We show that under this objective the $\pos$ is 1 and the pure $\poa$ is 2, for any $m\geq 2$.
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Correlation

MPG Unit:	Max-Planck-Institut für Informatik

MPG Subunit:	Algorithms and Complexity Group
Audience:	experts only
Appearance:	MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@ARTICLE{ChEpKS13,
AUTHOR = {Chen, Xujin and Epstein, Leah and Kleiman, Elena and van Stee, Rob},
TITLE = {Maximizing the minimum load: The cost of selfishness},
JOURNAL = {Theoretical Computer Science},
PUBLISHER = {Elsevier},
YEAR = {2013},
VOLUME = {482},
PAGES = {9--19},
MONTH = {April},
ISBN = {0304-3975},
}

Entry last modified by Rob van Stee, 02/17/2014

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	Editor(s) [Library]	Created 01/14/2014 03:54:39 PM
Revision 0.	Editor Rob van Stee	Edit Date 14/01/2014 15:54:39