On dynamic shortest paths problems

Liam Roditty*, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem. We also obtain slightly weaker results for the corresponding unweighted problems. (ii) A randomized fully-dynamic algorithm for the all-pairs shortest-paths problem in directed unweighted graphs with an amortized update time of \tilde {O}(m\sqrt{n}) (we use \tilde {O} to hide small poly-logarithmic factors) and a worst case query time is O(n 3/4). (iii) A deterministic O(n 2log∈n) time algorithm for constructing an O(log∈n)-spanner with O(n) edges for any weighted undirected graph on n vertices. The algorithm uses a simple algorithm for incrementally maintaining single-source shortest-paths tree up to a given distance.

Original languageEnglish
Pages (from-to)389-401
Number of pages13
Issue number2
StatePublished - Oct 2011


  • Dynamic algorithms
  • Graph
  • Shortest paths
  • Spanners


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