### 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(NM^{2}) 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 language | English |
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Pages | 446-452 |

Number of pages | 7 |

Publication status | Published - 1998 Dec 1 |

Event | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: 1998 Jan 25 → 1998 Jan 27 |

### Other

Other | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 98/1/25 → 98/1/27 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

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, .