## Abstract

Network's shortest paths calculation is an important need in transportation network analysis. The Dijkstra algorithm has long been developed for the shortest path of a pair of nodes calculation individually. A more practical method to simultaneously calculate all shortest paths of all pair of nodes of a network needs to be developed. This paper presents the development of a method to calculate simultaneously all shortest paths of all pairs of nodes of a network. This calculation method, called a Min-Plus Algebra, is a modification of Max-Plus Algebra, having a special Matrix Power Operation, enable and easier to be executed in spreadsheet software.

Original language | English |
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Pages (from-to) | 21-26 |

Number of pages | 6 |

Journal | Journal of Theoretical and Applied Information Technology |

Volume | 62 |

Issue number | 1 |

Publication status | Published - Apr 2014 |

## Keywords

- Matrix power operation
- Max-plus algebra
- Min-plus algebra
- Simultaneous shortest path calculation