Algorithms for the maximum subarray problem based on matrix multiplication

Hisao Tamaki, Takeshi Tokuyama

研究成果: Paper査読

44 被引用数 (Scopus)

抄録

Given an M×N array of reals, we want to find a rectangular contiguous subarray such that the sum of the entries in the subarray is maximized. Since Bentley posed this problem in his Programming Pearls column in 1984 with an O(NM2) time solution, no progress on the sequential complexity has been reported to date. We give the first subcubic algorithm, by reducing the problem to `funny matrix multiplication', where the scalar product and addition in usual matrix multiplication are replaced by addition and max operations, respectively. We also give a faster ε-approximation algorithm via the same reduction.

本文言語English
ページ446-452
ページ数7
出版ステータスPublished - 1998 12月 1
イベントProceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA
継続期間: 1998 1月 251998 1月 27

Other

OtherProceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms
CitySan Francisco, CA, USA
Period98/1/2598/1/27

ASJC Scopus subject areas

  • ソフトウェア
  • 数学 (全般)

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