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Stability and Recovery for Independence Systems

Authors Vaggos Chatziafratis, Tim Roughgarden, Jan Vondrak

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Vaggos Chatziafratis
Tim Roughgarden
Jan Vondrak

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Vaggos Chatziafratis, Tim Roughgarden, and Jan Vondrak. Stability and Recovery for Independence Systems. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ESA.2017.26

Abstract

Two genres of heuristics that are frequently reported to perform much better on "real-world" instances than in the worst case are greedy algorithms and local search algorithms. In this paper, we systematically study these two types of algorithms for the problem of maximizing a monotone submodular set function subject to downward-closed feasibility constraints. We consider perturbation-stable instances, in the sense of Bilu and Linial [11], and precisely identify the stability threshold beyond which these algorithms are guaranteed to recover the optimal solution. Byproducts of our work include the first definition of perturbation-stability for non-additive objective functions, and a resolution of the worst-case approximation guarantee of local search in p-extendible systems.

Subject Classification

Keywords
  • Submodular
  • approximation
  • stability
  • Local Search
  • Greedy
  • p-systems

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