Abstract
There has been recent progress in the selection problem, and in median-finding in particular, after a lull of ten years. This paper reviews some ancient and modern results on this problem, and suggests possibilities for future research.
This research was supported in part by the EU under contract 20244 (ALCOM-IT).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. W. Bent and J. W. John. Finding the median requires 2n comparisons. In Proc. 17th ACM Symp. on Theory of Computing, 1985, 213–216.
M. Blum, R. W. Floyd, V. R. Pratt, R. L. Rivest, and R. E. Tarjan. Time bounds for selection. J. Comput. Syst. Sci., 7, 1973, 448–461.
J. W. Daykin. Inequalities for the number of monotonie functions of partial orders. Discrete Mathematics, 61, 1986, 41–55.
D. E. Daykin, J. W. Daykin, and M. S. Paterson. On log concavity for order-preserving maps of partial orders. Discrete Mathematics, 50, 1984, 221–226.
D. Dor. Selection Algorithms. PhD thesis, Tel-Aviv University, 1995.
D. Dor and U. Zwick. Selecting the median. In Proc. 6th Annual ACM-SIAM Symp. on Discrete Algorithms, 1995, 28–37.
D. Dor and U. Zwick. Finding the αn th largest element. Combinatorica, 16, 1996, 41–58.
D. Dor and U. Zwick. Median selection requires (2+ε)n comparisons. Technical Report 312/96, April 1996, Department of Computer Science, Tel Aviv University.
F. Fussenegger and H. N. Gabow. A counting approach to lower bounds for selection problems. J. ACM, 26, 1978, 227–238.
A. Hadian and M. Sobel. Selecting the t th largest using binary errorless comparisons. Colloquia Mathematica Societatis János Bolyai, 4, 1969, 585–599.
L. Hyafil. Bounds for selection. SIAM J. on Computing, 5, 1976, 109–114.
J. W. John. The Complexity of Selection Problems. PhD thesis, University of Wisconsin at Madison, 1985.
D. G. Kirkpatrick. Topics in the complexity of combinatorial algorithms. Tech. Rep. 74, Dept. of Computer Science, University of Toronto, 1974.
D. G. Kirkpatrick. A unified lower bound for selection and set partitioning problems. J. ACM, 28, 1981, 150–165.
S. S. Kislitsyn. On the selection of the k th element of an ordered set by pairwise comparisons. Sibirsk. Mat. Zh., 5, 1964, 557–564. (In Russian.)
D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, Reading, MA, 1973.
T. Motoki. A note on upper bounds for the selection problem. Inf. Proc. Lett., 15, 1982, 214–219.
J. I. Munro and P. V. Poblete. A lower bound for determining the median. Technical Report Research Report CS-82-21, University of Waterloo, 1982.
V. Pratt and F. F. Yao. On lower bounds for computing the i th largest element. In Proc. 14th IEEE Symp. on Switching and Automata Theory, 1973, 70–81.
P. V. Ramanan and L. Hyafil. New algorithms for selection. J. Algorithms, 5, 1984, 557–578.
A. Schönhage, M. S. Paterson, and N. Pippenger. Finding the median. J. Comput. Syst. Sci., 13, 1976, 184–199.
J. Schreier. On tournament elimination systems. Mathesis Polska, 7, 1932, 154–160. (In Polish.)
F. F. Yao. On lower bounds for selection problems. Technical Report MAC TR-121, M.I.T., 1974.
C. K. Yap. New upper bounds for selection. Comm. ACM, 19, 1976, 501–508.
C. K. Yap. New lower bounds for medians and related problems. Computer Science Report 79, Yale University, 1976.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paterson, M. (1996). Progress in selection. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_146
Download citation
DOI: https://doi.org/10.1007/3-540-61422-2_146
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61422-7
Online ISBN: 978-3-540-68529-6
eBook Packages: Springer Book Archive