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
Volume7074 LNCS
DOIs
Publication statusPublished - 2011
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

Fingerprint

Knapsack
Knapsack Problem
Cardinality
Robustness
Computing
Fully Polynomial Time Approximation Scheme
Polynomials
Polynomial time
Quotient
NP-complete problem
Denote
Integer
Approximation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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 (Vol. 7074 LNCS, 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

Computing knapsack solutions with cardinality robustness. / Kakimura, Naonori; Makino, Kazuhisa; Seimi, Kento.

Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS 2011. p. 693-702 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS).

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

Kakimura, N, Makino, K & Seimi, K 2011, Computing knapsack solutions with cardinality robustness. in Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. vol. 7074 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7074 LNCS, pp. 693-702, 22nd International Symposium on Algorithms and Computation, ISAAC 2011, Yokohama, Japan, 11/12/5. https://doi.org/10.1007/978-3-642-25591-5_71
Kakimura N, Makino K, Seimi K. Computing knapsack solutions with cardinality robustness. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS. 2011. p. 693-702. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25591-5_71
Kakimura, Naonori ; Makino, Kazuhisa ; Seimi, Kento. / Computing knapsack solutions with cardinality robustness. Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS 2011. pp. 693-702 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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