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Maximizing the Minimum Load for Selfisch Agents

Authors Leah Epstein, Rob van Stee



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Leah Epstein
Rob van Stee

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Leah Epstein and Rob van Stee. Maximizing the Minimum Load for Selfisch Agents. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07261.10

Abstract

We consider the problem of maximizing the minimum load for machines that are controlled by selfish agents, who are only interested in maximizing their own profit. Unlike the classical load balancing problem, this problem has not been considered for selfish agents until now. For a constant number of machines, $m$, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a new technique for reducing the number of jobs while remaining close to the optimal solution. We also present an FPTAS for the classical machine covering problem, i.e., where no selfish agents are involved (the previous best result for this case was a PTAS) and use this to give a monotone FPTAS. Additionally, we give a monotone approximation algorithm with approximation ratio $min(m,(2+eps)s_1/s_m)$ where $eps>0$ can be chosen arbitrarily small and $s_i$ is the (real) speed of machine $i$. Finally we give improved results for two machines.
Keywords
  • Scheduling
  • algorithmic mechanism design
  • maximizing minimum load

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