A Robust PTAS for the Parallel Machine Covering Problem

Authors Martin Skutella, Jose Verschae



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Martin Skutella
Jose Verschae

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Martin Skutella and Jose Verschae. A Robust PTAS for the Parallel Machine Covering Problem. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09261.4

Abstract

In general, combinatorial optimization problems are unstable: slight changes on the instance of a problem can render huge changes in the optimal solution. Thus, a natural question arises: Can we achieve stability if we only maintain approximate solutions?. In this talk I will first formalize these ideas, and then show some results on the parallel machine covering problem. In particular I will derive a robust PTAS, i.e., I will show how to construct a solution that is not only $(1-epsilon)$-approximate, but is also stable. That is, if the instance is changed by adding or removing a job, then we can construct a new near-optimal solution by only slightly modifying the previous one.
Keywords
  • Stability
  • approximation schemes
  • online algorithms

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