License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.SOSA.2018.5
URN: urn:nbn:de:0030-drops-82994
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Chan, Timothy M.

Approximation Schemes for 0-1 Knapsack

OASIcs-SOSA-2018-5.pdf (0.5 MB)


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

  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 =		{},
  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
Collection: 1st Symposium on Simplicity in Algorithms (SOSA 2018)
Issue Date: 2018
Date of publication: 05.01.2018

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