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Mergesort and heapsort are comparison sorts which perform O(n log n) comparisons, so they are asymptotically optimal in this sense. If the input data have some a priori properties which can be exploited in construction of algorithms, in addition to comparisons, then asymptotically faster algorithms may be possible.
Merge sort's main advantages are that it is a stable sort and has excellent worst-case performance. The main disadvantage of merge sort is that it is an out-of-place algorithm, so when operating on arrays, efficient implementations require O ( n ) auxiliary space (vs. O (log n ) for quicksort with in-place partitioning and tail recursion, or O ...
External sorting algorithms generally fall into two types, distribution sorting, which resembles quicksort, and external merge sort, which resembles merge sort. External merge sort typically uses a hybrid sort-merge strategy. In the sorting phase, chunks of data small enough to fit in main memory are read, sorted, and written out to a temporary ...
Merge sort parallelizes well due to the use of the divide-and-conquer method. Several different parallel variants of the algorithm have been developed over the years. Some parallel merge sort algorithms are strongly related to the sequential top-down merge algorithm while others have a different general structure and use the K-way merge method.
A graph exemplifying merge sort. Two red arrows starting from the same node indicate a split, while two green arrows ending at the same node correspond to an execution of the merge algorithm. The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm. Conceptually, the merge sort algorithm ...
Batcher's odd–even mergesort [1] is a generic construction devised by Ken Batcher for sorting networks of size O(n (log n) 2) and depth O((log n) 2), where n is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in 1998, with respect to the AKS network that "Batcher's method is much better, unless n ...
External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead they must reside in the slower external memory (usually a hard drive). k-way merge algorithms usually take place in the second stage of external sorting algorithms, much like they do for merge sort.
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold.