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.ITCS.2020.49
URN: urn:nbn:de:0030-drops-117347
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11734/
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Makarychev, Konstantin ; Makarychev, Yury

Certified Algorithms: Worst-Case Analysis and Beyond

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LIPIcs-ITCS-2020-49.pdf (0.5 MB)

Abstract

In this paper, we introduce the notion of a certified algorithm. Certified algorithms provide worst-case and beyond-worst-case performance guarantees. First, a γ-certified algorithm is also a γ-approximation algorithm - it finds a γ-approximation no matter what the input is. Second, it exactly solves γ-perturbation-resilient instances (γ-perturbation-resilient instances model real-life instances). Additionally, certified algorithms have a number of other desirable properties: they solve both maximization and minimization versions of a problem (e.g. Max Cut and Min Uncut), solve weakly perturbation-resilient instances, and solve optimization problems with hard constraints.
In the paper, we define certified algorithms, describe their properties, present a framework for designing certified algorithms, provide examples of certified algorithms for Max Cut/Min Uncut, Minimum Multiway Cut, k-medians and k-means. We also present some negative results.

BibTeX - Entry

@InProceedings{makarychev_et_al:LIPIcs:2020:11734,
  author =	{Konstantin Makarychev and Yury Makarychev},
  title =	{{Certified Algorithms: Worst-Case Analysis and Beyond}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11734},
  URN =		{urn:nbn:de:0030-drops-117347},
  doi =		{10.4230/LIPIcs.ITCS.2020.49},
  annote =	{Keywords: certified algorithm, perturbation resilience, Bilu, Linial stability, beyond-worst-case analysis, approximation algorithm, integrality}
}

Keywords: certified algorithm, perturbation resilience, Bilu, Linial stability, beyond-worst-case analysis, approximation algorithm, integrality
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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