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View all- Abdelhafeez LCalderon-Romero AMagdy ATsotras V(2024)Pyneapple-G: Scalable Spatial Grouping QueriesProceedings of the VLDB Endowment10.14778/3685800.368590217:12(4469-4472)Online publication date: 8-Nov-2024
Scalable Overlay Operations over DCEL Polygon Layers
Pages 85 - 95
Abstract
The Doubly Connected Edge List (DCEL) is an edge-list structure that has been widely utilized in spatial applications for planar topological computations. An important operation is the overlay which combines the DCELs of two input layers and can easily support spatial queries like the intersection, union and difference between these layers. However, existing sequential implementations for computing the overlay do not scale and fail to complete for large datasets (for example the US census tracks). In this paper we propose a distributed and scalable way to compute the overlay operation and its related supported queries. We address the issues involved in efficiently distributing the overlay operator and offer various optimizations that improve performance. Our scalable solution can compute the overlay of very large real datasets (32M edges) in few minutes.
References
[1]
G. Barequet. 1998. DCEL - A Polyhedral Database and Programming Environment. IJCGA 08, 05n06 (1998), 619–636.
[2]
N. Beckmann, H. Kriegel, R. Schneider, and B. Seeger. 1990. The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles. In ACM SIGMOD PODS. Association for Computing Machinery, New York, NY, USA, 322–331.
[3]
E. Berberich, E. Fogel, D. Halperin, M. Kerber, and O. Setter. 2010. Arrangements on Parametric Surfaces. Mathematics in Computer Science 4, 1 (2010), 67–91.
[4]
M. Berg, O. Cheong, M. Kreveld, and M. Overmars. 2008. Computational Geometry: Algorithms and Applications. Springer, TU Eindhoven, P.O. Box 513.
[5]
P. Boguslawski, C. Gold, and H. Ledoux. 2011. Modelling and analysing 3D buildings with a primal/dual data structure. ISPRS 66, 2 (2011), 188–197.
[6]
D. Boltcheva, J. Basselin, C. Poull, H. Barthélemy, and D. Sokolov. 2020. Topological-based roof modeling from 3D point clouds. In WSCG, Vol. 28. Union Agency, Science Press, CZ 301 00 Plzen, 137–146.
[7]
J. Challa, P. Goyal, S. Nikhil, A. Mangla, S. Balasubramaniam, and N. Goyal. 2016. DD-Rtree: A dynamic distributed data structure for efficient data distribution among cluster nodes for spatial data mining algorithms. In IEEE Big Data. IEEE, 222 Rosewood Drive, Danvers, MA 01923., 27–36.
[8]
L. Chew and K. Kedem. 1993. A convex polygon among polygonal obstacles. Computational Geometry 3, 2 (1993), 59–89.
[9]
V. Chvátal. 1975. A combinatorial theorem in plane geometry. Combinatorial Theory 18, 1 (1975), 39–41.
[10]
R. Finkel and J. Bentley. 1974. Quad Trees: A Data Structure for Retrieval on Composite Keys.Acta Inf. 4 (1974), 1–9.
[11]
E. Fogel, D. Halperin, and R. Wein. 2012. CGAL Arrangements and Their Applications. Springer Berlin, Heidelberg.
[12]
W. Franklin, S. Magalhães, and M. Andrade. 2018. Data Structures for Parallel Spatial Algorithms on Large Datasets. In ACM BigSpatial. ACM, Seattle, WA, USA, 16–19.
[13]
W. Freiseisen. 1998. Colored DCEL for boolean operations in 2D.
[14]
A. Guttman. 1984. R-Trees: A Dynamic Index Structure for Spatial Searching. In ACM SIGMOD ICMD. Association for Computing Machinery, New York, NY, United States, 47–57.
[15]
R. Holmes. 2021. The DCEL Data Structure for 3D Graphics.
[16]
Y. Li, A. Eldawy, J. Xue, N. Knorozova, M. Mokbel, and R. Janardan. 2019. Scalable computational geometry in MapReduce. VLDB 28, 1 (2019), 523–548.
[17]
S. Magalhães, M. Andrade, W. Franklin, and W. Li. 2015. Fast exact parallel map overlay using a two-level uniform grid. In ACM BigSpatial. Association for Computing Machinery, New York, NY, USA, 45–54.
[18]
K. Mehlhorn and S. Näher. 1995. LEDA: a platform for combinatorial and geometric computing. Commun. ACM 38, 1 (1995), 96–102.
[19]
D. Muller and F. Preparata. 1978. Finding the intersection of two convex polyhedra. Theoretical Computer Science 7, 2 (1978), 217–236.
[20]
J. Nievergelt, H. Hinterberger, and K. Sevcik. 1984. The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Trans. Database Syst. 9, 1 (1984), 38–71.
[21]
J. O’Rourke. 1987. Art Gallery Theorems and Algorithms. Oxford University Press, United States.
[22]
F. Preparata and M. Shamos. 1985. Computational Geometry: An Introduction. Springer, New York, NY.
[23]
S. Puri, D. Agarwal, X. He, and S. Prasad. 2013. MapReduce Algorithms for GIS Polygonal Overlay Processing. In IEEE IPDPS. IEEE, Cambridge, MA, USA, 1009–1016.
[24]
S. Puri and S. Prasad. 2013. Efficient Parallel and Distributed Algorithms for GIS Polygonal Overlay Processing. In IEEE IPDPS. IEEE Computer Society, USA, 2238–2241.
[25]
I. Sabek and M. Mokbel. 2017. On Spatial Joins in MapReduce. In ACM SIGSPATIAL. Association for Computing Machinery, New York, NY, USA, 1–10.
[26]
H. Samet. 1990. The Design and Analysis of Spatial Data Structures. Wesley, 75 Arlington Street, Suite 300 Boston, MA, United States.
Index Terms
- Scalable Overlay Operations over DCEL Polygon Layers
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August 2023
204 pages
ISBN:9798400708992
DOI:10.1145/3609956
Copyright © 2023 Owner/Author.
This work is licensed under a Creative Commons Attribution-ShareAlike International 4.0 License.
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Association for Computing Machinery
New York, NY, United States
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Published: 24 August 2023
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View all- Abdelhafeez LCalderon-Romero AMagdy ATsotras V(2024)Pyneapple-G: Scalable Spatial Grouping QueriesProceedings of the VLDB Endowment10.14778/3685800.368590217:12(4469-4472)Online publication date: 8-Nov-2024
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