Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Chan, Timothy M. http://www.dagstuhl.de/oasics License
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URN: urn:nbn:de:0030-drops-82994
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Approximation Schemes for 0-1 Knapsack

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Abstract

We revisit the standard 0-1 knapsack problem. The latest polynomial-time approximation scheme by Rhee (2015) with approximation factor 1+eps has running time near O(n+(1/eps)^{5/2}) (ignoring polylogarithmic factors), and is randomized. We present a simpler algorithm which achieves the same result and is deterministic. With more effort, our ideas can actually lead to an improved time bound near O(n + (1/eps)^{12/5}), and still further improvements for small n.

BibTeX - Entry

@InProceedings{chan:OASIcs:2018:8299,
  author =	{Timothy M. Chan},
  title =	{{Approximation Schemes for 0-1 Knapsack}},
  booktitle =	{1st Symposium on Simplicity in Algorithms (SOSA 2018)},
  pages =	{5:1--5:12},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-064-4},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{61},
  editor =	{Raimund Seidel},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8299},
  URN =		{urn:nbn:de:0030-drops-82994},
  doi =		{10.4230/OASIcs.SOSA.2018.5},
  annote =	{Keywords: knapsack problem, approximation algorithms, optimization, (min,+)-convolution}
}

Keywords: knapsack problem, approximation algorithms, optimization, (min,+)-convolution
Seminar: 1st Symposium on Simplicity in Algorithms (SOSA 2018)
Issue date: 2018
Date of publication: 2018


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