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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.

MSC:
68P10 Searching and sorting
68W05 Nonnumerical algorithms
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