@inproceedings{4375,
abstract = {We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\
The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07).
We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range.
Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds.
Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.},
author = {Benter, Markus and Knollmann, Till and Meyer auf der Heide, Friedhelm and Setzer, Alexander and Sundermeier, Jannik},
booktitle = {Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD)},
keyword = {Distributed Storage, Multi-Dimensional Range Queries, Peer-to-Peer, Hilbert Curve},
location = {Helsinki},
title = {{A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension}},
doi = {10.1007/978-3-030-19759-9_4},
year = {2018},
}