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Optimizing stable in-place merging. (English) Zbl 1051.68050
Summary: In 2000, V. Geffert, J. Katajainen and T. Pasanen [Theor. Comput. Sci. 237, 159–181 (2000; Zbl 0939.68160)] presented an asymptotically efficient algorithm for stable merging in constant extra space. The algorithm requires at most \(m_1(t+1)+ m_2/2^t+o(m_1)\) comparisons \((t=\lfloor \log_2(m_2/m_1)\rfloor)\) and \(5m_2+12m_1+ o(m_1)\) moves, where \(m_1\) and \(m_2\) are the sizes of two ordered sublists to be merged, and \(m_1\leq m_2\). This paper optimizes the algorithm. The optimized algorithm is simpler than their algorithm, and makes at most \(m_1(t+1)+ m_2/2'+o(m_1+m_2)\) comparisons and \(6m_2+7m_1+ o(m_1+m_2)\) moves.

68P10 Searching and sorting
68W05 Nonnumerical algorithms
Full Text: DOI
[1] Dudzinski, K.; Dydek, A., On a stable minimum storage merging algorithm, Inform. process. lett., 12, 5-8, (1981) · Zbl 0453.68037
[2] Geffert, V.; Katajainen, J.; Pasanen, T., Asymptotically efficient in-place merging, Theoret. comput. sci., 237, 159-181, (2000) · Zbl 0939.68160
[3] Huang, B.-C.; Langston, 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] D.E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973. · Zbl 0302.68010
[7] Kronrod, M.A., An optimal ordering algorithm without operational field, Soviet math. dokl., 10, 744-746, (1969) · Zbl 0236.68017
[8] Mannila, H.; Ukkonen, E., Simple linear-time algorithm for in situ merging, Inform. process. lett., 18, 203-208, (1984)
[9] Salowe, J.S.; Steiger, W.L., Simplified stable merging tasks, J. algorithms, 8, 557-571, (1987) · Zbl 0641.68092
[10] Symvonis, A., Optimal stable merging, Comput. J., 38, 681-690, (1995)
[11] Trabb Pardo, L., Stable sorting and merging with optimal space and time bounds, SIAM J. comput., 6, 351-372, (1977) · Zbl 0356.68054
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