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**1 - 2**of**2**### Ratio based stable in-place merging

"... Abstract. We investigate the problem of stable in-place merging from a ratio k = n based point of view where m, n are the sizes of the input m sequences with m ≤ n. We introduce a novel algorithm for this problem that is asymptotically optimal regarding the number of assignments as well as compariso ..."

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Abstract. We investigate the problem of stable in-place merging from a ratio k = n based point of view where m, n are the sizes of the input m sequences with m ≤ n. We introduce a novel algorithm for this problem that is asymptotically optimal regarding the number of assignments as well as comparisons. Our algorithm uses knowledge about the ratio of the input sizes to gain optimality and does not stay in the tradition of Mannila and Ukkonen’s work [8] in contrast to all other stable in-place merging algorithms proposed so far. It has a simple modular structure and does not demand the additional extraction of a movement imitation buffer as needed by its competitors. For its core components we give concrete implementations in form of Pseudo Code. Using benchmarking we prove that our algorithm performs almost always better than its direct competitor proposed in [6]. As additional sub-result we show that stable in-place merging is a quite simple problem for every ratio k ≥ √ m by proving that there exists a primitive algorithm that is asymptotically optimal for such ratios. 1

### A Simple Algorithm for Stable Minimum Storage Merging

"... Abstract. We contribute to the research on stable minimum storage merging by introducing an algorithm that is particularly simply structured compared to its competitors. The presented algorithm performs O(m log ( n + 1)) comparisons and O((m + n) log m) assignments, where m m and n are the sizes of ..."

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Abstract. We contribute to the research on stable minimum storage merging by introducing an algorithm that is particularly simply structured compared to its competitors. The presented algorithm performs O(m log ( n + 1)) comparisons and O((m + n) log m) assignments, where m m and n are the sizes of the input sequences with m ≤ n. Hence, according to the lower bounds of merging the algorithm is asymptotically optimal regarding the number of comparisons. As central new idea we present a principle of symmetric splitting, where the start and end point of a rotation are computed by a repeated halving of two search spaces. This principle is structurally simpler than the principle of symmetric comparisons introduced earlier by Kim and Kutzner. It can be transparently implemented by few lines of Pseudocode. We report concrete benchmarks that prove the practical value of our algorithm. 1