Dijkstra's algorithm and L-concave function maximization

Kazuo Murota, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

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 languageEnglish
Pages (from-to)163-177
Number of pages15
JournalMathematical Programming
Volume145
Issue number1-2
DOIs
Publication statusPublished - 2014 Jun

Keywords

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

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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