Hybrid Bellman–Ford–Dijkstra algorithm

Yefim Dinitz, Rotem Itzhak

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We consider the single-source shortest paths problem in a digraph with negative edge costs allowed. A hybrid of the Bellman–Ford and Dijkstra algorithms is suggested, improving the running time bound of Bellman–Ford for graphs with a sparse distribution of negative cost edges. The algorithm iterates Dijkstra several times without re-initializing the tentative value d(v) at vertices. At most k+2 iterations solve the problem, if for any vertex reachable from the source, there exists a shortest path to it with at most k negative cost edges. In addition, a new, straightforward proof is suggested that the Bellman–Ford algorithm produces a shortest paths tree.

Original languageEnglish
Pages (from-to)35-44
Number of pages10
JournalJournal of Discrete Algorithms
StatePublished - 1 Jan 2017


  • Algorithm
  • Graph
  • Negative edge
  • Shortest path

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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