Stable Minimum Storage Merging by Symmetric Comparisons

We introduce a new stable minimum storage algorithm for merging that needs O(m log( n m +1)) element comparisons, where m and n are the sizes of the input sequences with m ≤ n. According to the lower bound for merging, our algorithm is asymptotically optimal regarding the number of comparisons. The presented algorithm rearranges the elements to be merged by rotations, where the areas to be rotated are determined by a simple principle of symmetric comparisons. This style of minimum storage merging is novel and looks promising. Our algorithm has a short and transparent definition. Experimental work has shown that it is very efficient and so might be of high practical interest.