Dynamic low-stretch spanning trees in subpolynomial time

Shiri Chechik, Tianyi Zhang

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

11 Scopus citations

Abstract

Low-stretch spanning tree has been an important graph-theoretic object, as it is one of the building blocks for fast algorithms that solve symmetrically diagonally dominant linear systems, and a significant line of research has been devoted to finding constructions with optimal average stretch. In a very recent work by Goranci and Forster [STOC 2019], the authors initiated the study of low-stretch spanning trees in the dynamic setting, and they proposed a dynamic algorithm that maintains a spanning tree in n12 +o(1) amortized update time with subpolynomial stretch in an unweighted graph on n vertices undergoing edge insertions and deletions demanded by an oblivious adversary. Our main results are twofold. First, we substantially improve the update time of Goranci and Forster [STOC 2019] from n12 +o(1) to a subpolynomial of no(1). Second, we generalize our result to weighted graphs under the decremental setting. As far as we know, this is the first non trivial dynamic algorithm for maintaining low-stretch spanning tree for weighted graphs.

Original languageEnglish
Title of host publication31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
EditorsShuchi Chawla
PublisherAssociation for Computing Machinery
Pages463-475
Number of pages13
ISBN (Electronic)9781611975994
StatePublished - 2020
Event31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States
Duration: 5 Jan 20208 Jan 2020

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2020-January

Conference

Conference31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/TerritoryUnited States
CitySalt Lake City
Period5/01/208/01/20

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