Fault-tolerant distance labeling for planar graphs

Aviv Bar-Natan, Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Research output: Contribution to journalArticlepeer-review


In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph G such that from the labels of any three vertices u,v,f we can infer the u-to-v distance in the graph G∖{f}. We show that any directed weighted planar graph (and in fact any graph in a graph family with O(n)-size separators, such as minor-free graphs) admits fault-tolerant distance labels of size O(n2/3). We extend these labels in a way that allows us to also count the number of shortest paths, and provide additional upper and lower bounds for labels and oracles for counting shortest paths.

Original languageEnglish
Pages (from-to)48-59
Number of pages12
JournalTheoretical Computer Science
StatePublished - 29 May 2022

Bibliographical note

Funding Information:
Supported in part by the Israel Science Foundation grant 810/21 .

Publisher Copyright:
© 2022 Elsevier B.V.


  • Counting shortest paths
  • Fault-tolerant distance labels
  • Forbidden-set distance labels
  • Planar graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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