Complexity Analysis of a Simple Algorithm for Stable Minimum Storage Merging

Abstract

We contribute to the research on complexity analysis of a stable minimum storage merging algorithm that is particularly simply structured and transparently implemented by few lines of Pseudocode compared to its competitors. The algorithm presented in [4] is based on a structurally simple principle of symmetric splitting, where the start and end point of a rotation are computed by a repeated halving of two search spaces. The algorithm performs ?logn?+1 comparisons in the best case and O(mlog(n/m))comparisons in the worst case, 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. For proving the worst case complexity we consider several special cases. Based on the complexity of these special cases we prove the worst case complexity of the algorithm.