Algorithms for the maximum subarray problem based on matrix multiplication

Hisao Tamaki, Takeshi Tokuyama

Research output: Contribution to conferencePaper

42 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages446-452
Number of pages7
Publication statusPublished - 1998 Dec 1
EventProceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA
Duration: 1998 Jan 251998 Jan 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

  • Software
  • Mathematics(all)

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    Tamaki, H., & Tokuyama, T. (1998). Algorithms for the maximum subarray problem based on matrix multiplication. 446-452. Paper presented at Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms, San Francisco, CA, USA, .