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 mapping 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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References
Alber, J., Niedermeier, R.: On multidimensional curves with hilbert property. Theory Comput. Syst. 33(4), 295–312 (2000). https://doi.org/10.1007/s002240010003
Albrecht, J., Oppenheimer, D., Vahdat, A., Patterson, D.A.: Design and implementation trade-offs for wide-area resource discovery. ACM Trans. Internet Technol. 8(4), 18:1–18:44 (2008). https://doi.org/10.1145/1391949.1391952
Andrzejak, A., Xu, Z.: Scalable, efficient range queries for grid information services. In: P2P 2002 Proceedings of the Second International Conference on Peer-to-Peer Computing, pp. 33–40 (2002). https://doi.org/10.1109/PTP.2002.1046310
Cai, M., Frank, M., Chen, J., Szekely, P.: MAAN: a multi-attribute addressable network for grid information services. J. Grid Comput. 2(1), 3–14 (2003). https://doi.org/10.1007/s10723-004-1184-y
Carlini, E., Lulli, A., Ricci, L.: DRAGON: multidimensional range queries on distributed aggregation trees. Future Gener. Comput. Syst. 55, 101–115 (2016). https://doi.org/10.1016/j.future.2015.07.020, http://www.sciencedirect.com/science/article/pii/S0167739X15002526
Datta, A., Hauswirth, M., John, R., Schmidt, R., Aberer, K.: Range queries in trie-structured overlays. In: P2P 2005 Proceedings of the Fifth IEEE International Conference on Peer-to-Peer Computing, pp. 57–66. IEEE (2005)
Ganesan, P., Yang, B., Garcia-Molina, H.: One torus to rule them all: multi-dimensional queries in P2P systems. In: WebDB 2004 Proceedings of the 7th International Workshop on the Web and Databases: Colocated with ACM SIGMOD/PODS 2004 WebDB 2004, pp. 19–24. ACM, New York (2004). https://doi.org/10.1145/1017074.1017081
Hilbert, D.: Über die stetige Abbildung einer Linie auf ein Flächenstück, pp. 1–2. Springer, Heidelberg (1935). https://doi.org/10.1007/978-3-662-38452-7-1
Jagadish, H.V., Ooi, B.C., Vu, Q.H.: Baton: a balanced tree structure for peer-to-peer networks. In: Proceedings of the 31st International Conference on Very Large Data Bases VLDB Endowment, pp. 661–672 (2005)
Lee, K., Choi, T., Boykin, P.O., Figueiredo, R.J.: MatchTree: flexible, scalable, and fault-tolerant wide-area resource discovery with distributed matchmaking and aggregation. Future Gener. Comput. Syst. 29(6), 1596–1610 (2013). https://doi.org/10.1016/j.future.2012.08.009, http://www.sciencedirect.com/science/article/pii/S0167739X12001653. including Special sections: High Performance Computing in the Cloud & Resource Discovery Mechanisms for P2P Systems
Li, D., Cao, J., Lu, X., Chen, K.C.C.: Efficient range query processing in peer-to-peer systems. IEEE Trans. Knowl. Data Eng. 21(1), 78–91 (2009). https://doi.org/10.1109/TKDE.2008.99
Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)
Naor, M., Wieder, U.: Novel architectures for P2P applications: the continuous-discrete approach. ACM Trans. Algorithms 3(3), 34 (2007). https://doi.org/10.1145/1273340.1273350
Pitoura, T., Ntarmos, N., Triantafillou, P.: Saturn: range queries, load balancing and fault tolerance in DHT data systems. IEEE Trans. Knowl. Data Eng. 24(7), 1313–1327 (2012). https://doi.org/10.1109/TKDE.2010.266
Ramabhadran, S., Ratnasamy, S., Hellerstein, J.M., Shenker, S.: Prefix hash tree: an indexing data structure over distributed hash tables. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing, January 2004
Schmidt, C., Parashar, M.: Squid: enabling search in DHT-based systems. J. Parallel Distrib. Comput. 68, 962–975 (2008)
Shen, H., Xu, C.Z.: Leveraging a compound graph-based DHT for multi-attribute range queries with performance analysis. IEEE Trans. Comput. 61(4), 433–447 (2012). https://doi.org/10.1109/TC.2011.30
Shu, Y., Ooi, B.C., Tan, K.L., Zhou, A.: Supporting multi-dimensional range queries in peer-to-peer systems. In: P2P 2005 Proceedings of the Fifth IEEE International Conference on Peer-to-Peer Computing, pp. 173–180, August 2005. https://doi.org/10.1109/P2P.2005.35
Stoica, I., et al.: Chord: a scalable peer-to-peer lookup protocol for internet applications. IEEE/ACM Trans. Network. 11(1), 17–32 (2003)
Zhang, C., Krishnamurthy, A., Wang, R.Y.: Skipindex: Towards a scalable peer-to-peer index service for high dimensional data. Technical report, Princeton University, May 2004
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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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