Abstract
The complexity of the problem of selecting the k-th element of a sorted matrix is known. In this note we show a lower bound for such a problem in sorted X+Y. This lower bound is tight since the upper bound for sorted matrices holds for sorted X+Y.
On leave from the University of Sao Paulo, Brazil. Member of the BID/USP project.
Preview
Unable to display preview. Download preview PDF.
References
M. Blum, R.W. Floyd, V. Pratt, R.L. Rivest and R.E. Tarjan, "Time bounds for selection", JCSS, 7 (1973), pp 448–461
M. Cosnard, J. Duprat and A.G. Ferreira, "The complexity of searching in X + Y and other multisets", Information Processing Letters, 34 (1990) 103–109
M.L.Fredman, "Two applications of a probabilistic search technique: sorting X + Y and building balanced search trees", in Proc. 7-th Annual ACM Symp. on Theory of Computing, (May 1975), ACM, 1975, pp 240–244
G.N. Frederickson and D.B. Johnson, "The complexity of selection and ranking in X + Y and matrices with sorted columns", JCSS 24 (1982), pp 197–208
G.N. Frederickson and D.B. Johnson, "Generalized selection and ranking: sorted matrices", SIAM J. Comput. 13 (1), Feb 1984, pp 197–208
L.H. Harper, T.H. Payne, J.E. Savage and E. Straus, "Sorting X + Y", Comm. ACM 18 (6) (1975), pp 347–349
J.L.Lambert, Sorting the elements of X+Y with O(n2) comparisons, in Proceedings of STACS 90, Feb. 1990, Rouens, France
N. Linial and M. Saks, "Searching ordered structures", Journal of Algorithms 6 (1985), pp 86–103
A. Mirzaian and E. Arjomandi, "Selection in X + Y and matrices with sorted rows and columns", Inf. Proc. Letters 20 (1985), pp 13–17
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cosnard, M., Ferreira, A.G. (1991). A tight lower bound for selection in sorted X+Y. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_162
Download citation
DOI: https://doi.org/10.1007/3-540-54029-6_162
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54029-8
Online ISBN: 978-3-540-47359-6
eBook Packages: Springer Book Archive