On dynamic approximate shortest paths for planar graphs with worst-case costs

Ittai Abraham, Shiri Chechik, Daniel Delling, Andrew V. Goldberg, Renato F. Werneck

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

14 Scopus citations

Abstract

Given a base weighted planar graph Ginput on n nodes and parameters M, ∈ we present a dynamic distance oracle with 1 + ∈ stretch and worst case update and query costs of ∈-3M4· poly-log(n). We allow arbitrary edge weight updates as long as the shortest path metric induced by the updated graph has stretch of at most M relative to the shortest path metric of the base graph Ginput. For example, on a planar road network, we can support fast queries and dynamic traffic updates as long as the shortest path from any source to any target (including using arbitrary detours) is between, say, 80 and 3 miles-per-hour. As a warm-up we also prove that graphs of bounded treewidth have exact distance oracles in the dynamic edge model. To the best of our knowledge, this is the first dynamic distance oracle for a non-trivial family of dynamic changes to planar graphs with worst case costs of o(n1-2) both for query and for update operations.

Original languageEnglish
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Pages740-753
Number of pages14
ISBN (Electronic)9781510819672
DOIs
StatePublished - 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: 10 Jan 201612 Jan 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2

Conference

Conference27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Country/TerritoryUnited States
CityArlington
Period10/01/1612/01/16

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