Comments on parallel algorithms for the knapsack problem

  • Authors:

  • Carlos Alberto Alonso Sanches;Nei Yoshihiro Soma;Horacio Hideki Yanasse

  • Affiliations:

  • Instituto Tecnológico de Aeronáutica--CTA/ITA/IEC, Pça. Mal. Eduardo Gomes, 50 S.J. Campos, SP 12.228-900, Brazil;Instituto Tecnológico de Aeronáutica--CTA/ITA/IEC, Pça. Mal. Eduardo Gomes, 50 S.J. Campos, SP 12.228-900, Brazil;Instituto Nacional de Pesquisas Espaciais--INPE/LAC, Av. dos Astronautas, 1758--Jardim da Granja, S.J. Campos, SP 12227-010, Brazil

  • Venue:
  • Parallel Computing
  • Year:
  • 2002

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Abstract

Chang et al. [Parallel Comput. (1994) 233] introduced a parallel algorithm based on a shared memory SIMD architecture for the generation phase of the classic Horowitz and Sahni [J. ACM 21(2) (1974) 277] two-list serial algorithm for the knapsack problem. They claimed that their parallel generation phase could be accomplished in time O((n/8)2) and in space O(2n/4) with O(2n/8) processors.We prove that their results are not correct, i.e., that the suggested scheme time and space complexity should be bounded, instead, by O(n2n/2) and O(2n/2), respectively. These results also invalidate the performance analysis of the more recent Lou and Chang [Parallel Comput. (1997) 1985] algorithm.