Abstract
We present a peer-to-peer network that supports the efficient processing of orthogonal range queries 
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 map** of the Hilbert Curve through \([m]^d\) to the peers.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center ‘On-The-Fly Computing’ (SFB 901).
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Benter, M., Knollmann, T., auf der Heide, F.M., Setzer, A., Sundermeier, J. (2019). A Peer-to-Peer Based Cloud Storage Supporting Orthogonal Range Queries of Arbitrary Dimension. In: Disser, Y., Verykios, V. (eds) Algorithmic Aspects of Cloud Computing. ALGOCLOUD 2018. Lecture Notes in Computer Science(), vol 11409. Springer, Cham. https://doi.org/10.1007/978-3-030-19759-9_4
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