License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2017.26
URN: urn:nbn:de:0030-drops-78423
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Chatziafratis, Vaggos ; Roughgarden, Tim ; Vondrak, Jan

Stability and Recovery for Independence Systems

LIPIcs-ESA-2017-26.pdf (0.6 MB)


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.

BibTeX - Entry

  author =	{Vaggos Chatziafratis and Tim Roughgarden and Jan Vondrak},
  title =	{{Stability and Recovery for Independence Systems}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-78423},
  doi =		{10.4230/LIPIcs.ESA.2017.26},
  annote =	{Keywords: Submodular, approximation, stability, Local Search, Greedy, p-systems}

Keywords: Submodular, approximation, stability, Local Search, Greedy, p-systems
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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