Computing knapsack solutions with cardinality robustness

Naonori Kakimura, Kazuhisa Makino, Kento Seimi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In this paper, we study the robustness over the cardinality variation for the knapsack problem. For the knapsack problem and a positive number α ≤ 1, we say that a feasible solution is α-robust if, for any positive integer k, it includes an α-approximation of the maximum k-knapsack solution, where a k-knapsack solution is a feasible solution that consists of at most k items. In this paper, we show that, for any ε > 0, the problem of deciding whether the knapsack problem admits a (ν + ε)-robust solution is weakly NP-hard, where ν denotes the rank quotient of the corresponding knapsack system. Since the knapsack problem always admits a ν-robust knapsack solution [7], this result provides a sharp border for the complexity of the robust knapsack problem. On the positive side, we show that a max-robust knapsack solution can be computed in pseudo-polynomial time, and present a fully polynomial time approximation scheme (FPTAS) for computing a max-robust knapsack solution.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
Pages693-702
Number of pages10
DOIs
Publication statusPublished - 2011 Dec 26
Externally publishedYes
Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
Duration: 2011 Dec 52011 Dec 8

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7074 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd International Symposium on Algorithms and Computation, ISAAC 2011
CountryJapan
CityYokohama
Period11/12/511/12/8

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kakimura, N., Makino, K., & Seimi, K. (2011). Computing knapsack solutions with cardinality robustness. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings (pp. 693-702). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_71