Though the behaviors of mergesort algorithms are basically known, the periodicity phenomena encountered in their analyses are not easy to deal with. In this paper closed-form expressions for the necessary number of comparisons are derived for the bottom-up algorithm, which adequately describe its periodic behavior. This allows, among other things, to compare the top-down and the bottom-up
... [Show full abstract] mergesort algorithms. Keywords: Sorting, mergesort; analysis of algorithms. 1. Introduction Mergesort is one of the most prominent internal sorting methods. Especially for lists it is one of the best available alternatives (cf. [Knuth], [Gonnet]). Among the particular advantages of mergesort --- also compared to Quicksort and its variants --- it maintains its O(N log N) time complexity also in the worst case (in fact the worst case time is only O(N) worse than the average time) and it is stable. There are two basic variants of mergesort, namely top-down mergesort and bottomup mergesort. Yet anoth...