1 research outputs found
Strategies for Stable Merge Sorting
We introduce new stable natural merge sort algorithms, called -merge sort
and -merge sort. We prove upper and lower bounds for several merge sort
algorithms, including Timsort, Shivers' sort, -stack sorts, and our new
-merge and -merge sorts. The upper and lower bounds have the forms
and for inputs of length~ comprising
~monotone runs. For Timsort, we prove a lower bound of . For -merge sort, we prove optimal upper and lower bounds of
approximately . We prove similar asymptotically
matching upper and lower bounds for -merge sort, when , where is the golden ratio.
Our bounds are in terms of merge cost; this upper bounds the number of
comparisons and accurately models runtime. The merge strategies can be used for
any stable merge sort, not just natural merge sorts. The new -merge and
-merge sorts have better worst-case merge cost upper bounds and are
slightly simpler to implement than the widely-used Timsort; they also perform
better in experiments. We report also experimental comparisons with algorithms
developed by Munro-Wild and Jug\'e subsequently to the results of the present
paper.Comment: 38 pages, 5 figure