eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-10-07
19:1
19:16
10.4230/LIPIcs.DISC.2020.19
article
Improved Hardness of Approximation of Diameter in the CONGEST Model
Grossman, Ofer
1
Khoury, Seri
2
Paz, Ami
3
MIT, Cambridge, MA, USA
University of California, Berkeley, CA, USA
Faculty of Computer Science, Universität Wien, Austria
We study the problem of approximating the diameter D of an unweighted and undirected n-node graph in the congest model. Through a connection to extremal combinatorics, we show that a (6/11 + ε)-approximation requires Ω(n^{1/6}/log n) rounds, a (4/7 + ε)-approximation requires Ω(n^{1/4}/log n) rounds, and a (3/5 + ε)-approximation requires Ω(n^{1/3}/log n) rounds. These lower bounds are robust in the sense that they hold even against algorithms that are allowed to return an additional small additive error. Prior to our work, only lower bounds for (2/3 + ε)-approximation were known [Frischknecht et al. SODA 2012, Abboud et al. DISC 2016].
Furthermore, we prove that distinguishing graphs of diameter 3 from graphs of diameter 5 requires Ω(n/log n) rounds. This stands in sharp contrast to previous work: while there is an algorithm that returns an estimate ⌊ 2/3D ⌋ ≤ D̃ ≤ D in Õ(√n+D) rounds [Holzer et al. DISC 2014], our lower bound implies that any algorithm for returning an estimate 2/3D ≤ D̃ ≤ D requires ̃Ω(n) rounds.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol179-disc2020/LIPIcs.DISC.2020.19/LIPIcs.DISC.2020.19.pdf
Distributed graph algorithms
Approximation algorithms
Lower bounds