Formulation of the addition-shift-sequence problem and its complexity

Akihiro Matsuura, Akira Nagoya

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

1 Citation (Scopus)

Abstract

Given a sequence of integers, what is the smallest number of additions and shifts needed to compute all integers starting with 1? This is a generalization of the addition-sequence problem which naturally appears in the multiplication of constants with a single variable and in its hardware implementation, and it will be called the addition-shift- sequence problem. As a fundamental result on computational complexity, we show that the addition-shift-sequence problem is NP-complete. Then, we show lower and upper bounds of the number of operations for some particular sequence, where some techniques specific to our model are demonstrated.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages43-51
Number of pages9
Volume1350
ISBN (Print)3540638903, 9783540638902
DOIs
Publication statusPublished - 1997
Externally publishedYes
Event8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 - Singapore, Singapore
Duration: Dec 17 1997Dec 19 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1350
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th Annual International Symposium on Algorithms and Computation, ISAAC 1997
CountrySingapore
CitySingapore
Period12/17/9712/19/97

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Matsuura, A., & Nagoya, A. (1997). Formulation of the addition-shift-sequence problem and its complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1350, pp. 43-51). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1350). Springer Verlag. https://doi.org/10.1007/3-540-63890-3_6