Fully dynamic all-pairs shortest paths with worst-case update-time revisited

Ittai Abraham, Shiri Chechik, Sebastian Krinninger

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

43 Scopus citations

Abstract

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worstcase guarantees on the time needed to process a single update (in contrast to related results, the update time is not amortized over a sequence of updates). Our main result is a simple randomized algorithm that for any parameter c > 1 has a worst-case update time of O(cn2+2/3 log4/3 n) and answers distance queries correctly with probability 1 - 1/nc, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of O(n2+3/4) and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds.

Original languageEnglish
Title of host publication28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
EditorsPhilip N. Klein
PublisherAssociation for Computing Machinery
Pages440-452
Number of pages13
ISBN (Electronic)9781611974782
DOIs
StatePublished - 2017
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain
Duration: 16 Jan 201719 Jan 2017

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume0

Conference

Conference28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
Country/TerritorySpain
CityBarcelona
Period16/01/1719/01/17

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