Fault-Tolerant Distance Labeling for Planar Graphs

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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
Title of host publicationStructural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings
EditorsTomasz Jurdziński, Stefan Schmid
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
ISBN (Print)9783030795269
StatePublished - 2021
Event28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021 - Virtual, Online
Duration: 28 Jun 20211 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12810 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021
CityVirtual, Online

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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