Distance oracles beyond the thorup-zwick bound

Mihai Pátraşcu, Liam Roditty

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


We give the first improvement to the space/approximation trade-off of distance oracles since the seminal result of Thorup and Zwick. For unweighted undirected graphs, our distance oracle has size O(n5/3) and, when queried about vertices at distance d, returns a path of length at most 2d +1. For weighted undirected graphs with m = n2/a edges, our distance oracle has size O(n2/ 3 v α) and returns a factor 2 approximation. Based on a plausible conjecture about the hardness of set intersection queries, we show that a 2-approximate distance oracle requires space ~Ω&(n2/ v α). For unweighted graphs, this implies a ~Ω&(n1.5) space lower bound to achieve approximation 2d + 1.

Original languageEnglish
Pages (from-to)300-311
Number of pages12
JournalSIAM Journal on Computing
Issue number1
StatePublished - 2014


  • Distance oracles
  • Lower bounds
  • Set intersection
  • Shortest paths


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