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/m + 1)) comparisons and O((m + n) log m) assignments, where 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. © Springer-Verlag Berlin Heidelberg 2007.