Algorithms and hardness for diameter in dynamic graphs
Name
LIPIcs-ICALP-2019-13.pdf
Description
Published version
Size
515.01 KB
Format
Adobe PDF
Checksum (MD5)
107eb48f74bd9f9796db9dfd6bdc1a8e
Author(s)
Williams, Virginia Vassilevska
Ancona, Bertie
Wein, Nicole
Date Issued
2019
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Williams, Virginia Vassilevska, Ancona, Bertie and Wein, Nicole. 2019. "Algorithms and hardness for diameter in dynamic graphs." Leibniz International Proceedings in Informatics, LIPIcs, 132.
Version
Final published version
Abstract
© Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, and Nicole Wein; licensed under Creative Commons License CC-BY The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each update or from solving dynamic All-Pairs Shortest Paths (APSP), which is very computationally intensive. This is the situation for dynamic approximation algorithms as well, and even if only edge insertions or edge deletions need to be supported. This paper provides a comprehensive study of the dynamic approximation of Diameter, Radius and Eccentricities, providing both conditional lower bounds, and new algorithms whose bounds are optimal under popular hypotheses in fine-grained complexity. Some of the highlights include: Under popular hardness hypotheses, there can be no significantly better fully dynamic approximation algorithms than recomputing the answer after each update, or maintaining full APSP. Nearly optimal partially dynamic (incremental/decremental) algorithms can be achieved via efficient reductions to (incremental/decremental) maintenance of Single-Source Shortest Paths. For instance, a nearly (3/2+ε)-approximation to Diameter in directed or undirected n-vertex, medge graphs can be maintained decrementally in total time m1+o(1)√n/ε2. This nearly matches the static 3/2-approximation algorithm for the problem that is known to be conditionally optimal.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ICALP.2019.13
