ABSTRACT
We consider the orthogonal range aggregation problem. The dataset S consists of N axis-parallel rectangles in R2, each of which is associated with an integer weight. Given an axis-parallel rectangle Q and an aggregate function F, a query reports the aggregated result of the weights of the rectangles in S intersecting Q. The goal is to preprocess S into a structure such that all queries can be answered efficiently. We present indexing schemes to solve the problem in external memory when F = max (hence, min) and F = sum (hence, count and average), respectively. Our schemes have linear or near-linear space, and answer a query in O(logBN) or O(logB2/BN) I/Os, where B is the disk block size.
- P. Afshani, L. Arge, and K. D. Larsen. Orthogonal range reporting in three and higher dimensions. In Proceedings of Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 149--158, 2009. Google Scholar
Digital Library
- P. Afshani, L. Arge, and K. D. Larsen. Orthogonal range reporting: query lower bounds, optimal structures in 3-d, and higher-dimensional improvements. In Symposium on Computational Geometry (SoCG), pages 240--246, 2010. Google Scholar
Digital Library
- P. K. Agarwal, L. Arge, J. Yang, and K. Yi. I/O-efficient structures for orthogonal range-max and stabbing-max queries. In Proceedings of European Symposium on Algorithms (ESA), pages 7--18, 2003.Google Scholar
Cross Ref
- P. K. Agarwal, L. Arge, and K. Yi. An optimal dynamic interval stabbing-max data structure? In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 803--812, 2005. Google Scholar
Digital Library
- A. Aggarwal and J. S. Vitter. The input/output complexity of sorting and related problems. Communications of the ACM (CACM), 31(9):1116--1127, 1988. Google Scholar
Digital Library
- S. Alstrup, G. S. Brodal, and T. Rauhe. New data structures for orthogonal range searching. In Proceedings of Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 198--207, 2000. Google Scholar
Digital Library
- L. Arge. The buffer tree: A technique for designing batched external data structures. Algorithmica, 37(1):1--24, 2003.Google Scholar
Digital Library
- L. Arge and J. Vahrenhold. I/O-efficient dynamic planar point location. Computational Geometry, 29(2):147--162, 2004. Google Scholar
Digital Library
- L. Arge and J. S. Vitter. Optimal dynamic interval management in external memory. In Proceedings of Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 560--569, 1996. Google Scholar
Digital Library
- B. Chazelle. An algorithm for segment-dragging and its implementation. Algorithmica, 3:205--221, 1988.Google Scholar
Digital Library
- B. Chazelle. A functional approach to data structures and its use in multidimensional searching. SIAM Journal of Computing, 17(3):427--462, 1988. Google Scholar
Digital Library
- H. Edelsbrunner and M. H. Overmars. On the equivalence of some rectangle problems. Information Processing Letters (IPL), 14(3):124--127, 1982.Google Scholar
- S. Govindarajan, P. K. Agarwal, and L. Arge. CRB-tree: An efficient indexing scheme for range-aggregate queries. In Proceedings of International Conference on Database Theory (ICDT), pages 143--157, 2003. Google Scholar
Digital Library
- H. Kaplan, E. Molad, and R. E. Tarjan. Dynamic rectangular intersection with priorities. In Proceedings of ACM Symposium on Theory of Computing (STOC), pages 639--648, 2003. Google Scholar
Digital Library
- I. Lazaridis and S. Mehrotra. Progressive approximate aggregate queries with a multi-resolution tree structure. In Proceedings of ACM Management of Data (SIGMOD), pages 401--412, 2001. Google Scholar
Digital Library
- D. Papadias, P. Kalnis, J. Zhang, and Y. Tao. Efficient OLAP operations in spatial data warehouses. In Proceedings of Symposium on Advances in Spatial and Temporal Databases (SSTD), pages 443--459, 2001. Google Scholar
Digital Library
- B. Salzberg and V. J. Tsotras. Comparison of access methods for time-evolving data. ACM Computing Surveys, 31(2):158--221, 1999. Google Scholar
Digital Library
- Y. Tao and D. Papadias. Range aggregate processing in spatial databases. IEEE Transactions on Knowledge and Data Engineering (TKDE), 16(12):1555--1570, 2004. Google Scholar
Digital Library
- J. S. Vitter. Algorithms and data structures for external memory. Foundation and Trends in Theoretical Computer Science, 2(4):305--474, 2006. Google Scholar
Digital Library
- D. Zhang, A. Markowetz, V. J. Tsotras, D. Gunopulos, and B. Seeger. On computing temporal aggregates with range predicates. ACM Transactions on Database Systems (TODS), 33(2), 2008. Google Scholar
Digital Library
- D. Zhang and V. J. Tsotras. Optimizing spatial min/max aggregations. The VLDB Journal, 14(2):170--181, 2005. Google Scholar
Digital Library
Index Terms
New results on two-dimensional orthogonal range aggregation in external memory
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