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  A Note on Hardness of Diameter Approximation

Bringmann, K., & Krinninger, S. (2017). A Note on Hardness of Diameter Approximation. Retrieved from http://arxiv.org/abs/1705.02127.

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 Creators:
Bringmann, Karl1, Author           
Krinninger, Sebastian2, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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Free keywords: Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
 Abstract: We revisit the hardness of approximating the diameter of a network. In the CONGEST model, $ \tilde \Omega (n) $ rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al. DISC 2016 extended this result to sparse graphs and, at a more fine-grained level, showed that, for any integer $ 1 \leq \ell \leq \operatorname{polylog} (n) $, distinguishing between networks of diameter $ 4 \ell + 2 $ and $ 6 \ell + 1 $ requires $ \tilde \Omega (n) $ rounds. We slightly tighten this result by showing that even distinguishing between diameter $ 2 \ell + 1 $ and $ 3 \ell + 1 $ requires $ \tilde \Omega (n) $ rounds. The reduction of Abboud et al. is inspired by recent conditional lower bounds in the RAM model, where the orthogonal vectors problem plays a pivotal role. In our new lower bound, we make the connection to orthogonal vectors explicit, leading to a conceptually more streamlined exposition. This is suited for teaching both the lower bound in the CONGEST model and the conditional lower bound in the RAM model.

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Language(s): eng - English
 Dates: 2017-05-052017
 Publication Status: Published online
 Pages: 11 p.
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1705.02127
URI: http://arxiv.org/abs/1705.02127
BibTex Citekey: DBLP:journals/corr/BringmannK17
 Degree: -

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