## Abstract

We study the average-case complexity of min-sum product of matrices, which is a fundamental operation that has many applications in computer science. We focus on optimizing the number of “algebraic” operations (i.e., operations involving real numbers) used in the computation, since such operations are usually expensive in various environments. We present an algorithm that can compute the min-sum product of two n × n real matrices using only O(n^{2}) algebraic operations, given that the matrix elements are drawn independently and identically from some fixed probability distribution satisfying several constraints. This improves the previously best known upper-bound of O(n^{2} log n). The class of probability distributions under which our algorithm works include many important and commonly used distributions, such as uniform distributions, exponential distributions, and folded normal distributions.

In order to evaluate the performance of the proposed algorithm, we performed experiments to compare the running time of the proposed algorithm with algorithms in[7]. The experimental results demonstrate that our algorithm achieves significant performance improvement over the previous algorithms.

Original language | English |
---|---|

Title of host publication | Algorithms and Computation: 25th International Symposium, ISAAC 2014, Proceedings |

Editors | Hee-Kap AHN, Chan-Su SHIN |

Place of Publication | Switzerland |

Publisher | Springer, Cham |

Pages | 41-52 |

Number of pages | 12 |

ISBN (Electronic) | 9783319130750 |

ISBN (Print) | 9783319130743 |

DOIs | |

Publication status | Published - 8 Nov 2014 |

Externally published | Yes |

Event | Algorithms and computation : 25th International Symposium, ISAAC 2014 - Jeonju, Korea, Republic of Duration: 15 Dec 2014 → 17 Dec 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 8889 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Symposium

Symposium | Algorithms and computation : 25th International Symposium, ISAAC 2014 |
---|---|

Country/Territory | Korea, Republic of |

City | Jeonju |

Period | 15/12/14 → 17/12/14 |