• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.272-277
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• 2008

Symmerge is a stable minimum storage merging algorithm that needs $O(m{\log}{\frac{n}{m}})$ element comparisons, where in and n are the sizes of the input sequences with $m{\leq}n$. Hence, according to the lower bound for merging, the algorithm is asymptotically optimal regarding the number of comparisons. The Symmerge algorithm is based on the standard recursive technique of "divide and conquer". The objective of this paper is to consider the relationship between m and n for the degenerated case where the recursion depth reaches m-1.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.455-462
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• 2010

We investigate the worst case complexity regarding the number of comparisons for a simple and stable merging algorithm. The complexity analysis shows that the algorithm performs O(mlog(n/m)) comparisons for two sequences of sizes m and n $m{\leq}n$. So, according to the lower bound for merging $\Omega$(mlog(n/m)), the algorithm is asymptotically optimal regarding the number of comparisons. For proving the worst case complexity we divide the domain of all inputs into two disjoint cases. For either of these cases we will extract a special subcase and prove the asymptotic optimality for these two subcases. Using this knowledge for special cases we will prove the optimality for all remaining cases. By using this approach we give a transparent solution for the hardly tractable problem of delivering a clean complexity analysis for the algorithm.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.53-56
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• 2007

Symmerge is a stable minimum storage algorithm for merging that needs $O(mlog\frac{n}{m})$ element comparisons, where m and n are the sizes of the input sequences with m ${\leqq}$ n. According to the lower bound for merging, the algorithm is asymptotically optimal regarding the number of comparisons. The objective of this paper is to consider the relationship between m and n for the spanning case with the recursion level m-1.