Distributed Distance Approximation
Name
LIPIcs-OPODIS-2020-30.pdf
Description
Published version
Size
575.1 KB
Format
Adobe PDF
Checksum (MD5)
af78b78d3e15325ff14021e24c72e8e2
Author(s)
Ancona, B
Censor-Hillel, K
Dalirrooyfard, M
Efron, Y
Williams, VV
Date Issued
January 1, 2021
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Ancona, B, Censor-Hillel, K, Dalirrooyfard, M, Efron, Y and Williams, VV. 2021. "Distributed Distance Approximation." Leibniz International Proceedings in Informatics, LIPIcs, 184.
Version
Final published version
Abstract
© Bertie Ancona, Keren Censor-Hillel, Mina Dalirrooyfard, Yuval Efron, and Virginia Vassilevska Williams; licensed under Creative Commons License CC-BY 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact solutions. In this paper, we give a near complete characterization of the trade-offs between approximation ratios and round complexity of distributed algorithms for approximating these parameters, with a focus on the weighted and directed variants. Furthermore, we study bi-chromatic variants of these parameters defined on a graph whose vertices are colored either red or blue, and one focuses only on distances for pairs of vertices that are colored differently. Motivated by applications in computational geometry, bi-chromatic diameter, radius and eccentricities have been recently studied in the sequential setting [Backurs et al. STOC'18, Dalirrooyfard et al. ICALP'19]. We provide the first distributed upper and lower bounds for such problems. Our technical contributions include introducing the notion of approximate pseudo-center, which extends the pseudo-centers of [Choudhary and Gold SODA'20], and presenting an efficient distributed algorithm for computing approximate pseudo-centers. On the lower bound side, our constructions introduce the usage of new functions into the framework of reductions from 2-party communication complexity to distributed algorithms.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.OPODIS.2020.30
