## Abstract

Dijkstra's algorithm is a well-known algorithm for the single-source shortest path problem in a directed graph with nonnegative edge length. We discuss Dijkstra's algorithm from the viewpoint of discrete convex analysis, where the concept of discrete convexity called L-convexity plays a central role. We observe first that the dual of the linear programming (LP) formulation of the shortest path problem can be seen as a special case of L-concave function maximization. We then point out that the steepest ascent algorithm for L-concave function maximization, when applied to the LP dual of the shortest path problem and implemented with some auxiliary variables, coincides exactly with Dijkstra's algorithm.

Original language | English |
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Pages (from-to) | 163-177 |

Number of pages | 15 |

Journal | Mathematical Programming |

Volume | 145 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2014 Jun |

## Keywords

- Dijkstra's algorithm
- Discrete concave function
- Shortest path problem
- Steepest ascent algorithm

## ASJC Scopus subject areas

- Software
- Mathematics(all)