Abstract
This paper presents vectorized methods of construction and descent of quadtrees that can be easily adapted to message passing parallel computing. A time complexity analysis for the present approach is also discussed. The proposed method of tree construction requires a hash table to index nodes of a linear quadtree in the breadth-first order. The hash is performed in two steps: an internal hash to index child nodes and an external hash to index nodes in the same level (depth). The quadtree descent is performed by considering each level as a vector segment of a linear quadtree, so that nodes of the same level can be processed concurrently.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Finkel, R.A., Bentley, J.L.: Quad Trees: A data structure for retrieval on composite keys. Acta Inf. 4, 1–9 (1974)
Gaede, V., Günther, O.: Multidimensional access methods. ACM Computing Surveys 2(30), 170–231 (1998)
Poulakidas, A.S., Srinivasan, A., Eğecioğlu, Ö., Ibarra, O., Yang, T.: Image compression for fast wavelet-based subregion retrieval. Theoretical Computer Science 240(2), 447–469 (2000)
Fischer, A., Bar-Yoseph, P.Z.: Adaptive mesh generation based on multi-resolution quadtree representation. International Journal For Numerical Methods In Engineering 48, 1571–1582 (2000)
Schustere, G.M., Katsaggelos, A.K.: An optimal quadtree-based motion estimation and motion-compensated interpolation scheme for video compression. IEEE Transactions on Image Processing 7(11), 1505–1523 (1998)
Ichinose, N., Yada, T., Takagi, T.: Quadtree representation of DNA sequences. Genome Informatics 12, 510–511 (2001)
McNaughton, M., Lu, P., Schaeffer, J., Szafron, D.: Memory-efficient A* heuristics for multiple sequence alignment. In: Proceedings of the Eighteenth National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, July 28-August, pp. 737–743. AAAI Press, Edmonton (2002)
Callahan, P.B.: Optimal parallel all-nearest-neighbors using the well-separated pair decomposition. In: Proc. 34th Symp. Foundations of Computer Science, pp. 332–340. IEEE (1993)
Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching in fixed dimensions. J. ACM 45(6), 891–923 (1998)
Barnes, J., Hut, P.: A hierarchical O(N log N) force-calculation algorithm. Nature 324, 446–449 (1986)
Warren, M.S., Salmon, J.K.: A parallel hashed tree N-body algorithm. In: ACM Proceedings, Supercomputing 1993, November 15-19, pp. 12–21. ACM Press, Portland (1993)
Warren, M.S., Salmon, J.K.: A portable parallel particle program. Comput. Phys. Comm. (87), 266–290 (1995)
Marinho, E.P., Lépine, J.R.D.: SPH simulations of clumps formation by dissipative collision of molecular clouds. I. Non magnetic case. Astronomy and Astrophysics Supplement 142, 165–179 (2000)
Marinho, E.P., Andreazza, C.M., Lépine, J.R.D.: SPH simulations of clumps formation by dissipative collisions of molecular clouds. II. Magnetic case. Astronomy and Astrophysics 379, 1123–1137 (2001)
Samet, H.: The design and analysis of spatial data structures. Addison-Wesley Longman Publishing Co., Inc. (1990)
Hung, Y., Rosenfeld, A.: Parallel processing of linear quadtrees on a mesh-connected computer. J. Parallel Distrib. Comput. 7(1), 1–27 (1989)
Mason, D.: Linear quadtree algorithms for transputer array. IEEE Proceedings of Computers and Digital Techniques 137(1), 114–128 (1990)
Dehne, F., Ferreira, A.G., Rau-chaplin, A.: Parallel processing of pointer based quadtrees on hypercube multiprocessors. In: Proc. International Conference on Parallel Processing (1991)
Yang, S., Lee, R.: Efficient parallel nighbor finding algorithms for quadtrees on hypercube. Journal of Information Science and Engineering 9, 81–102 (1993)
Bhaskar, S.K., Rosenfeld, A., Wu, A.Y.: Parallel processing of regions represented by linear quadtrees. Computer Vision, Graphics, and Image Processing 42(3), 371–380 (1988)
Gargantini, I.: An effective way to represent quadtrees. Commun. ACM 25(12), 905–910 (1982)
Hernquist, L.: Vectorization of Tree Traversals. Journal of Computational Physics 87, 137–147 (1990)
N-body algorithm. In: ACM, editor, Proceedings, Supercomputing 1993, Portland, Oregon, November 15-19, pp. 12–21. ACM Press (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marinho, E.P., Baldassin, A. (2012). Vectorized Algorithms for Quadtree Construction and Descent. In: Xiang, Y., Stojmenovic, I., Apduhan, B.O., Wang, G., Nakano, K., Zomaya, A. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2012. Lecture Notes in Computer Science, vol 7439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33078-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-33078-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33077-3
Online ISBN: 978-3-642-33078-0
eBook Packages: Computer ScienceComputer Science (R0)