This Article 
 Bibliographic References 
 Add to: 
Clustering on a Hypercube Multicomputer
April 1991 (vol. 2 no. 2)
pp. 129-137

Squared error clustering algorithms for single-instruction multiple-data (SIMD) hypercubes are presented. The algorithms are shown to be asymptotically faster than previously known algorithms and require less memory per processing element (PE). For a clustering problem with N patterns, M features per pattern, and K clusters, the algorithms complete in O(k+log NM) steps on NM processor hypercubes. This is optimal up to a constant factor. These results are extended to the case in which NMK processors are available. Experimental results from a multiple-instruction, multiple-data (MIMD) medium-grain hypercube are also presented.

[1] D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[2] E. Dekel, D. Nassimi, and S. Sahni, "Parallel matrix and graph algorithms,"SIAM J. Comput., pp. 657-675, 1981.
[3] R. O. Duda and P. E. Hart,Pattern Classification and Scene Analysis.New York: Wiley, 1973.
[4] T.H. Dunigan, "Hypercube performance," inHypercube Multiprocessors.M. T. Heath, Ed., SIAM, 1987, pp. 178-192.
[5] K.S. Fu,Syntactic Methods in Pattern Recognition.New York: Academic, 1974.
[6] K. Fukunaga,Introduction to Statistical Pattern Recognition. New York: Academic, 1972.
[7] K. Hwang and D. Kim. "Parallel pattern clustering on a multiprocessor with orthogonally shared memory," inProc. 1987 Int. Conf. Parallel Processing, pp. 913-916.
[8] X. Li and Z. Fang, "Parallel algorithms for clustering on hypercube SIMD computers," inProc. 1986 Conf. Computer Vision Pattern Recognition, 1986, pp. 130-133.
[9] D. Nassimi and S. Sahni, "Data broadcasting in SIMD computers,"IEEE Trans. Comput., vol. C-30, pp. 101-107, Feb. 1981.
[10] L. M. Ni and A. K. Jain, "A VLSI systolic architecture for pattern clustering,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI- 7, no. 1, pp. 80-89, Jan. 1985.
[11] S. Ranka and S. Sahni, "Image template matching on an SIMD hypercube multicomputer," Univ. of Minnesota Tech. Rep., 1987.
[12] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.
[13] J. T. Tou and R. C. Gonzalez,Pattern Recognition Principles.Reading MA: Addison-Wesley, 1974.

Index Terms:
Index Termssquare error; hypercube multicomputer; single-instruction multiple-data; SIMD; clustering problem; NMK processors; multiple-instruction, multiple-data; MIMD; computational complexity; hypercube networks; parallel algorithms
S. Ranka, S. Sahni, "Clustering on a Hypercube Multicomputer," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 2, pp. 129-137, April 1991, doi:10.1109/71.89059
Usage of this product signifies your acceptance of the Terms of Use.