Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels

Ittai Abraham, Shiri Chechik, Cyril Gavoille

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels of length λ = O(ε -1 log 2n log(nM) · maxlogn). Given the labels of two vertices s and t and of a set F of faulty vertices/edges, our scheme approximates the distance between s and t in G \ F with stretch (1+ε), in O(|F| 2 λ) time. We then present a general method to transform (1+ε) forbidden-set labeling schemas into a fully dynamic (1+ε) distance oracle. Our fully dynamic (1+ε) distance oracle is of size O(n log{n} · maxlogn) and has Õ(n 1/2) query and update time, both the query and the update time are worst case. This improves on the best previously known (1+ε) dynamic distance oracle for planar graphs, which has worst case query time Õ(n 2/3) and amortized update time of Õ(n 2/3). Our (1+ε) forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch (1+ε).

Original languageEnglish
Title of host publicationSTOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages1199-1217
Number of pages19
DOIs
StatePublished - 2012
Externally publishedYes
Event44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States
Duration: 19 May 201222 May 2012

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/TerritoryUnited States
CityNew York, NY
Period19/05/1222/05/12

Keywords

  • distance oracle
  • dynamic algorithms
  • planar graphs

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