Playing tetris on meshes and multi-dimensional Shearsort
Shearsort is a classical sorting algorithm working in rounds on 2-dimensional meshes of processors. Its elementary and elegant runtime analysis can be found in various textbooks. There is a straightforward generalization of Shearsort to multi-dimensional meshes. As experiments turn out, it works fast. However, no method has yet been shown strong enough to provide a tight analysis of this algorithm. In this paper, we present an analysis of the 3-dimensional case and show that on the l x l x l-mesh, it suffices to perform 21ogl+ 10 rounds while 2logl+1 rounds are necessary. Moreover, tools for analyzing multi-dimensional Shearsort are provided.
KeywordsSorting Algorithm Left Endpoint Original Segment Parallel Sorting Oblivious Algorithm
Unable to display preview. Download preview PDF.
- 1.K. E. Batcher. Sorting networks and their applications. In AFIPS Conf Proc. 32, pp. 307–314, 1968.Google Scholar
- 2.K. Brockmann and R. Wanka. Efficient oblivious parallel sorting on the MasPar MP-l. In Proc. 30th IEEE HICSS, Vol. 1, pp. 200–208, 1997.Google Scholar
- 3.P. F. Corbett and I. D. Scherson. Sorting in mesh connected multiprocessors. IEEE Trans. Parallel and Distributed Systems 3 (1992) 626–632.Google Scholar
- 4.M. Dowd, Y. Perl, M. Saks, and L. Rudolph. The periodic balanced sorting network. J. ACM 36 (1989) 738–757.Google Scholar
- 5.D. E. Knuth. The Art of Computer Programming, Volume 3: Sorting and Searching (Addison-Wesley, Reading, 1973).Google Scholar
- 6.M. Kunde. Optimal sorting on multi-dimensionally mesh-connected computers. In Proc. 4th STACS, pp. 408–419, 1987.Google Scholar
- 7.F. T Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes (Morgan Kaufmann, San Mateo, 1992).Google Scholar
- 8.C. G. Plaxton. A hypercubic network with nearly logarithmic depth. In Proc. 24th ACM STOC, pp. 405–416, 1992.Google Scholar
- 9.I. D. Scherson and S. Sen. Parallel sorting in two-dimensional VLSI models of computation, IEEE Trans. Comput. 38 (1989) 238–249.Google Scholar
- 10.I. D. Scherson, S. Sen, and A. Shamir. Shear-sort: A true two-dimensional sorting technique for VLSI networks, in Proc. 15th IEEE ICPP, 1986, pp. 903–908.Google Scholar
- 11.C. P. Schnorr and A. Shamir. An optimal sorting algorithm for mesh-connected computers. In Proc. 18th ACM STOC, pp. 255–263, 1986.Google Scholar