@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)}},
  keywords     = {{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}},
}