research-article

Theoretically optimal and empirically efficient r-trees with strong parallelizability

Authors:

Yanchuan Chang,

Rui ZhangAuthors Info & Claims

Proceedings of the VLDB Endowment, Volume 11, Issue 5

Pages 621 - 634

https://doi.org/10.1145/3187009.3177738

Published: 01 January 2018 Publication History

Abstract

The massive amount of data and large variety of data distributions in the big data era call for access methods that are efficient in both query processing and index bulk-loading, and over both practical and worst-case workloads. To address this need, we revisit a classic multidimensional access method - the R-tree. We propose a novel R-tree packing strategy that produces R-trees with an asymptotically optimal I/O complexity for window queries in the worst case. Our experiments show that the R-trees produced by the proposed strategy are highly efficient on real and synthetic data of different distributions. The proposed strategy is also simple to parallelize, since it relies only on sorting. We propose a parallel algorithm for R-tree bulk-loading based on the proposed packing strategy, and analyze its performance under the massively parallel communication model. Experimental results confirm the efficiency and scalability of the parallel algorithm over large data sets.

References

[1]

http://www.pokemongo.com.

[2]

http://en.wikipedia.org/wiki/Google_Search.

[3]

https://www.wired.com/2016/09/pokemon-go-just-fine-without/.

[4]

http://www.microsoft.com/sqlserver/2008/en/us/spatial-data.aspx.

[5]

http://download.oracle.com/otndocs/products/spatial/pdf/spatial_features_jsirev.pdf.

[6]

https://www.cse.ust.hk/~yike/prtree/.

[7]

http://madalgo.au.dk/tpie/.

[8]

https://nectar.org.au/.

[9]

https://www.census.gov/geo/maps-data/data/tiger-line.html.

[10]

D. Achakeev, M. Seidemann, M. Schmidt, and B. Seeger. Sort-based parallel loading of r-trees. In 1st ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data, pages 62--70, 2012.

Digital Library

[11]

P. K. Agarwal, L. Arge, O. Procopiuc, and J. S. Vitter. A framework for index bulk loading and dynamization. In 28th International Colloquium on Automata, Languages and Programming, pages 115--127, 2001.

Digital Library

[12]

P. K. Agarwal, M. de Berg, J. Gudmundsson, M. Hammar, and H. J. Haverkort. Box-trees and r-trees with near-optimal query time. In 17th Annual Symposium on Computational Geometry (SCG), pages 124--133, 2001.

Digital Library

[13]

P. K. Agarwal, K. Fox, K. Munagala, and A. Nath. Parallel algorithms for constructing range and nearest-neighbor searching data structures. In PODS, pages 429--440, 2016.

Digital Library

[14]

A. Andoni, A. Nikolov, K. Onak, and G. Yaroslavtsev. Parallel algorithms for geometric graph problems. In STOC, pages 574--583, 2014.

Digital Library

[15]

L. Arge, M. D. Berg, H. Haverkort, and K. Yi. The priority r-tree: A practically efficient and worst-case optimal r-tree. ACM Transactions on Algorithms, 4(1):9:1--9:30, 2008.

Digital Library

[16]

P. Beame, P. Koutris, and D. Suciu. Communication steps for parallel query processing. In PODS, pages 273--284, 2013.

Digital Library

[17]

N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger. The r*-tree: An efficient and robust access method for points and rectangles. In SIGMOD, pages 322--331, 1990.

Digital Library

[18]

J. L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509--517, 1975.

Digital Library

[19]

S. Berchtold, D. A. Keim, and H.-P. Kriegel. The x-tree : An index structure for high-dimensional data. In VLDB, pages 28--39, 1996.

Digital Library

[20]

M. Berg, M. Kreveld, M. Overmars, and O. C. Schwarzkopf. Computational Geometry. Springer Berlin Heidelberg, 2000.

[21]

B. Chazelle. Functional approach to data structures and its use in multidimensional searching. SIAM Journal on Computing, 17(3):427--462, 1988.

Digital Library

[22]

J. Dean and S. Ghemawat. Mapreduce: Simplified data processing on large clusters. Communications of the ACM, 51(1):107--113, 2008.

Digital Library

[23]

D. J. DeWitt, N. Kabra, J. Luo, J. M. Patel, and J.-B. Yu. Client-server paradise. In VLDB, pages 558--569, 1994.

Digital Library

[24]

H. N. Gabow, J. L. Bentley, and R. E. Tarjan. Scaling and related techniques for geometry problems. In STOC, pages 135--143, 1984.

Digital Library

[25]

V. Gaede and O. Günther. Multidimensional access methods. ACM Computing Surveys, 30(2):170--231, 1998.

Digital Library

[26]

Y. J. García R, M. A. López, and S. T. Leutenegger. A greedy algorithm for bulk loading r-trees. In 6th ACM International Symposium on Advances in Geographic Information Systems, pages 163--164, 1998.

Digital Library

[27]

M. T. Goodrich. Communication-efficient parallel sorting. SIAM Journal on Computing, 29(2):416--432, 1999.

Digital Library

[28]

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In J. M. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, pages 87--106, 1999.

Digital Library

[29]

A. Guttman. R-trees: A dynamic index structure for spatial searching. In SIGMOD, pages 47--57, 1984.

Digital Library

[30]

H. Haverkort and F. V. Walderveen. Four-dimensional hilbert curves for r-trees. Journal of Experimental Algorithmics, 16:1--19, 2008.

Digital Library

[31]

H. V. Jagadish. Spatial search with polyhedra. In ICDE, pages 311--319, 1990.

Digital Library

[32]

H. V. Jagadish. Analysis of the hilbert curve for representing two-dimensional space. Information Processing Letters, 62(1):17--22, 1997.

Digital Library

[33]

I. Kamel and C. Faloutsos. Parallel r-trees. In SIGMOD, pages 195--204, 1992.

Digital Library

[34]

I. Kamel and C. Faloutsos. Hilbert r-tree: An improved r-tree using fractals. In VLDB, pages 500--509, 1994.

Digital Library

[35]

K. V. R. Kanth and A. K. Singh. Optimal dynamic range searching in non-replicating index structures. In ICDT, pages 257--276, 1999.

Digital Library

[36]

N. Koudas, C. Faloutsos, and I. Kamel. Declustering spatial databases on a multi-computer architecture. In EDBT, pages 592--614, 1996.

Digital Library

[37]

S. T. Leutenegger, J. M. Edgington, and M. A. Lopez. STR: A simple and efficient algorithm for r-tree packing. Technical report, 1997.

Digital Library

[38]

A. Mondal, M. Kitsuregawa, B. C. Ooi, and K. L. Tan. R-tree-based data migration and self-tuning strategies in shared-nothing spatial databases. In 9th ACM International Symposium on Advances in Geographic Information Systems, pages 28--33, 2001.

Digital Library

[39]

B. Moon, H. V. Jagadish, C. Faloutsos, and J. H. Saltz. Analysis of the clustering properties of the hilbert space-filling curve. IEEE Transactions on Knowledge and Data Engineering, 13(1):124--141, 2001.

Digital Library

[40]

Y. Ohsawa and M. Sakauchi. A new tree type data structure with homogeneous nodes suitable for a very large spatial database. In ICDE, pages 296--303, 1990.

Digital Library

[41]

J. A. Orenstein and T. H. Merrett. A class of data structures for associative searching. In PODS, pages 181--190, 1984.

Digital Library

[42]

A. Papadopoulos and Y. Manolopoulos. Parallel bulk-loading of spatial data. Parallel Computing, 29(10):1419--1444, 2003.

Digital Library

[43]

N. Roussopoulos and D. Leifker. Direct spatial search on pictorial databases using packed r-trees. In SIGMOD, pages 17--31, 1985.

Digital Library

[44]

B. Schnitzer and S. T. Leutenegger. Master-client r-trees: a new parallel r-tree architecture. In SSDBM, pages 68--77, 1999.

Digital Library

[45]

T. K. Sellis, N. Roussopoulos, and C. Faloutsos. The r+-tree: A dynamic index for multi-dimensional objects. In VLDB, pages 507--518, 1987.

Digital Library

[46]

Y. Tao, W. Lin, and X. Xiao. Minimal mapreduce algorithms. In SIGMOD, pages 529--540, 2013.

Digital Library

[47]

P. Xu and S. Tirthapura. Optimality of clustering properties of space-filling curves. ACM Transactions on Database Systems, 39(2):10:1--10:27, 2014.

Digital Library

[48]

S. You, J. Zhang, and L. Gruenwald. Parallel spatial query processing on gpus using r-trees. In 2nd ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data, pages 23--31, 2013.

Digital Library

[49]

M. Zaharia, M. Chowdhury, M. J. Franklin, S. Shenker, and I. Stoica. Spark: Cluster computing with working sets. In 2nd USENIX Conference on Hot Topics in Cloud Computing, pages 10--10, 2010.

Digital Library

[50]

R. Zhang, P. Kalnis, B. C. Ooi, and K. Tan. Generalized multidimensional data mapping and query processing. ACM Transactions on Database Systems, 30(3):661--697, 2005.

Digital Library

[51]

R. Zhang, B. C. Ooi, and K.-L. Tan. Making the pyramid technique robust to query types and workloads. In ICDE, pages 313--324, 2004.

Digital Library

[52]

R. Zhang, J. Qi, M. Stradling, and J. Huang. Towards a painless index for spatial objects. ACM Transactions on Database Systems, 39(3):19:1--19:42, 2014.

Digital Library

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Gu TFeng KYang JCong GLong CZhang R(2024)BT-Tree: A Reinforcement Learning Based Index for Big Trajectory DataProceedings of the ACM on Management of Data10.1145/36771302:4(1-27)Online publication date: 30-Sep-2024
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Theoretically optimal and empirically efficient r-trees with strong parallelizability
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Published In

cover image Proceedings of the VLDB Endowment

Proceedings of the VLDB Endowment Volume 11, Issue 5

January 2018

274 pages

ISSN:2150-8097

Editors:
Jian Pei
Simon Fraser University
,
Sihem Amer-Yahia
University of Grenoble Alpes, CNRS

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VLDB Endowment

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Published: 01 January 2018

Published in PVLDB Volume 11, Issue 5

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Cited By

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https://dl.acm.org/doi/10.1145/3677130
Li MWang HDai HLi MChai CGu RChen FChen ZLi SLiu QChen G(2024)A Survey of Multi-Dimensional Indexes: Past and Future TrendsIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.336418336:8(3635-3655)Online publication date: 1-Aug-2024
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Yang JCong G(2023)PLATON: Top-down R-tree Packing with Learned Partition PolicyProceedings of the ACM on Management of Data10.1145/36267421:4(1-26)Online publication date: 12-Dec-2023
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Gu TFeng KCong GLong CWang ZWang S(2023)The RLR-Tree: A Reinforcement Learning Based R-Tree for Spatial DataProceedings of the ACM on Management of Data10.1145/35889171:1(1-26)Online publication date: 30-May-2023
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Huang SWang YLi G(2023)ACR-Tree: Constructing R-Trees Using Deep Reinforcement LearningDatabase Systems for Advanced Applications10.1007/978-3-031-30637-2_6(80-96)Online publication date: 17-Apr-2023
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Xiao MWang HGeng LLee RZhang X(2022)An RDMA-enabled In-memory Computing Platform for R-tree on ClustersACM Transactions on Spatial Algorithms and Systems10.1145/35035138:2(1-26)Online publication date: 12-Feb-2022
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