×

zbMATH — the first resource for mathematics

Asymptotically efficient in-place merging. (English) Zbl 0939.68160
Summary: Two linear-time algorithms for in-place/merging are presented. Both algorithms perform at most \(m(t+1)+n/2^{t}+o(m)\) comparisons, where m and n are the sizes of the input sequences, \(m<n\), and \(t=\lfloor\log_{2} (n/m)\rfloor\). The first algorithm is for unstable/ merging and it carries out no more than \(3(n+m)+o(m)\) element moves. The second algorithm is for stable/merging and it accomplishes at most \(5n+12m+o(m)\) moves.

MSC:
68W05 Nonnumerical algorithms
68P10 Searching and sorting
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dudziński, K.; Dydek, A., On stable minimum storage merging algorithm, Inform. process. lett., 12, 5-8, (1981) · Zbl 0453.68037
[2] S. Dvořák, B. Ďurian, Towards an efficient merging, Proceedings of the 12th Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, vol. 233, Springer, Berlin, 1986, pp. 290-298.
[3] Huang, B-C.; Langston, M.A., Practical in-place merging, Comm. ACM, 31, 348-352, (1988)
[4] Huang, B-C.; Langston, M.A., Fast stable merging and sorting in constant extra space, Comput. J., 35, 643-650, (1992)
[5] Hwang, F.K.; Lin, S., A simple algorithm for merging two disjoint linearly ordered sets, SIAM J. comput., 1, 31-39, (1972) · Zbl 0235.68015
[6] Katajainen, J.; Pasanen, T.; Teuhola, J., Practical in-place mergesort, Nordic J. comput., 3, 27-40, (1996)
[7] D.E. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973. · Zbl 0302.68010
[8] Kronrod, M.A., Optimal ordering algorithm without operational field, Soviet math. dokl., 10, 744-746, (1969) · Zbl 0236.68017
[9] Mannila, H.; Ukkonen, E., A simple linear-time algorithm for in situ merging, Inform. process. lett., 18, 203-208, (1984)
[10] Munro, J.I.; Raman, V., Sorting with minimum data movement, J. algorithms, 13, 374-393, (1992) · Zbl 0772.68023
[11] Munro, J.I.; Raman, V., Selection from Read-only memory and sorting with minimum data movement, Theoret. comput. sci., 165, 311-323, (1996) · Zbl 0872.68045
[12] T. Pasanen, Lajittelu minimitilassa, M.Sc. Thesis T-93-3, Department of Computer Science, University of Turku, Turku, 1993.
[13] Salowe, J.S.; Steiger, W.L., Simplified stable merging tasks, J. algorithms, 8, 557-571, (1987) · Zbl 0641.68092
[14] Stockmeyer, P.K.; Yao, F.F., On the optimality of linear merge, SIAM J. comput., 9, 85-90, (1980) · Zbl 0446.68059
[15] Symvonis, A., Optimal stable merging, Comput. J., 38, 681-690, (1995)
[16] Trabb Pardo, L., Stable sorting and merging with optimal space and time bounds, SIAM J. comput., 6, 351-372, (1977) · Zbl 0356.68054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.