Abstract
Sequential selection has been solved in linear time by Blum e.a. Running this algorithm on a problem of size N with N > M, the size of the main-memory, results in an algorithm that reads and writes \( \mathcal{O}(N) \) elements, while the number of comparisons is also bounded by \( \mathcal{O}(N) \) . This is asymptotically optimal, but the constants are so large that in practice sorting is faster for most values of M and N.
This paper provides the first detailed study of the external selection problem. A randomized algorithm of a conventional type is close to optimal in all respects. Our deterministic algorithm is more or less the same, but first the algorithm builds an index structure of all the elements. This effort is not wasted: the index structure allows the retrieval of elements so that we do not need a second scan through all the data. This index structure can also be used for repeated selections, and can be extended over time. For a problem of size N, the deterministic algorithm reads N + o(N) elements and writes only o(N) elements and is thereby optimal to within lower-order terms.
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References
Aggarwal, A., J.S. Vitter, ‘The Input/Output Complexity of Sorting and Related Problems,’ Communications of the ACM, 31(9), pp. 1116–1127, 1988.
Blum, M., R.W. Floyd, V.R. Pratt, R.L. Rivest, R.E. Tarjan, ‘Time Bounds for Selection,’ Journal of Computing System Sciences, 7(4), pp. 448–461, 1972.
Carlsson, S., M. Sundström, ‘Linear-Time In-Place Selection in Less than 3n Comparisons,’ Proc. 6th International Symposium on Algorithms and Computation, LNCS 1004, pp. 245–253, Springer-Verlag, 1995.
Chaudhuri, S., T. Hagerup, R. Raman, ‘Approximate and Exact Deterministic Parallel Selection,’ Proc. 18th Symposium on Mathematical Foundations of Computer Science, LNCS 711, pp. 352–361, Springer-Verlag, 1993.
Dor, D., U. Zwick, ‘Selecting the Median,’ Proc. 6th Symposium on Discrete Algorithms, pp. 28–37, ACM-SIAM, 1995.
Floyd, R.W., R.L. Rivest, ‘Expected Time Bounds for Selection,’ Communications of the ACM, 18(3), pp. 165–172, 1975.
Nodine, M.H., J.S. Vitter, ‘Deterministic Distribution Sort in Shared and Distributed Memory Multiprocessors,’ Proc. 5th Symposium on Parallel Algorithms and Architectures, pp. 120–129, ACM, 1993.
Rajasekaran, S., ‘Randomized Parallel Selection,’ Proc. Foundations of Software Technology and Theoretical Computer Science, LNCS 472, pp. 215–223, Springer-Verlag, 1990.
Sibeyn, J.F., ‘Sample Sort on Meshes,’ Proc. 3rd Euro-Par Conference, LNCS 1300, pp. 389–398, Springer-Verlag, 1997.
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© 1999 Springer-Verlag Berlin Heidelberg
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Sibeyn, J.F. (1999). External Selection. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_27
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DOI: https://doi.org/10.1007/3-540-49116-3_27
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