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Approximation Schemes for 0-1 Knapsack

Author Timothy M. Chan



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Timothy M. Chan

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Timothy M. Chan. Approximation Schemes for 0-1 Knapsack. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 5:1-5:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/OASIcs.SOSA.2018.5

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.
Keywords
  • knapsack problem
  • approximation algorithms
  • optimization
  • (min,+)-convolution

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