New pseudopolynomial complexity bounds for the bounded and other integer Knapsack related problems

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Abstract

We consider the bounded integer knapsack problem (BKP) max ∑j = 1n pj xj, subject to: ∑j = 1n wj xj ≤ C, and xj ∈ {0, 1, ..., mj}, j = 1, ..., n. We use proximity results between the integer and the continuous versions to obtain an O (n3 W2) algorithm for BKP, where W = maxj = 1, ..., n wj. The respective complexity of the unbounded case with mj = ∞, for j = 1, ..., n, is O (n2 W2). We use these results to obtain an improved strongly polynomial algorithm for the multicover problem with cyclical 1's and uniform right-hand side.

Original languageEnglish
Pages (from-to)303-306
Number of pages4
JournalOperations Research Letters
Volume37
Issue number5
DOIs
StatePublished - Sep 2009

Keywords

  • Bounded knapsack problem
  • Bounded multiple-choice knapsack problem
  • Multicover problem
  • Pseudopolynomial algorithms

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