This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Parallel Construction of Multidimensional Binary Search Trees
February 2000 (vol. 11 no. 2)
pp. 136-148

Abstract—Multidimensional binary search tree (abbreviated k-d tree) is a popular data structure for the organization and manipulation of spatial data. The data structure is useful in several applications including graph partitioning, hierarchical applications such as molecular dynamics and $n$-body simulations, and databases. In this paper, we study efficient parallel construction of k-d trees on coarse-grained distributed memory parallel computers. We consider several algorithms for parallel k-d tree construction and analyze them theoretically and experimentally, with a view towards identifying the algorithms that are practically efficient. We have carried out detailed implementations of all the algorithms discussed on the CM-5 and report on experimental results.

[1] I. Al-furaih, S. Aluru, S. Goil, and S. Ranka, “Practical Algorithms for Selection on Coarse-Grained Parallel Computers,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 8, pp. 313-324, Aug. 1997.
[2] J.L. Bentley, “Multidimensional Binary Search Trees in Database Applications,” IEEE Trans. Software Eng., vol. 5, pp. 333-340, 1979.
[3] J.L. Bentley, "Multidimensional Binary Search Trees Used for Associative Searching," Comm. ACM, vol. 18, no. 9, pp. 509-517, 1975.
[4] G.E. Blelloch,Vector Models for Data-Parallel Computing. The MIT Press, 1990.
[5] M. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest, and R.E. Tarjan, “Time Bounds for Selection,” J. Computer Systems Science, vol. 7, pp. 448-461, 1972.
[6] F. Ercal, "Heuristic Approaches to Task Allocation for Parallel Computing," PhD thesis, Ohio State Univ., 1988.
[7] R.W. Floyd and R.L. Rivest, "Expected Time Bounds for Selection," Comm. ACM, vol. 18, no. 3, pp. 165-172, 1975.
[8] G. Foxet al.,Solving Problems on Concurrent Processors, vol. I. Englewood Cliffs, NJ: Prentice Hall, 1988.
[9] V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin Cummings, 1994.
[10] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[11] S. Rajasekharan, W. Chen, and S. Yooseph, “Unifying Themes for Parallel Selection,” Proc. Fifth Int'l Symp. Algorithms and Computation, 1994.
[12] S. Ranka, R.V. Shankar, and K.A. Alsabti, “Many-to-Many Communication with Bounded Traffic,” Proc. Frontiers of Massively Parallel Computation, pp. 20-27, 1995.
[13] A. Schonhage, M.S. Paterson, and N. Pippenger, “Finding the Median,” J. Computer Systems Science, vol. 13, pp. 184-199, 1976.
[14] H. Shi and J. Schaeffer, “Parallel Sorting by Regular Sampling,” J. Parallel and Distributed Computing, vol. 14, pp. 361-370, 1992.

Index Terms:
k-d trees, hypercubes, meshes, multidimensional binary search trees, parallel algorithms, parallel computers.
Citation:
Ibraheem Al-furaih, Srinivas Aluru, Sanjay Goil, Sanjay Ranka, "Parallel Construction of Multidimensional Binary Search Trees," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 2, pp. 136-148, Feb. 2000, doi:10.1109/71.841750
Usage of this product signifies your acceptance of the Terms of Use.