Library sort: Difference between revisions

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{{cite journal | journal=Theory of Computing Systems | volume=39 | issue=3 | pages=391 | year=2006 | author=Bender, M. A., Farach-Colton, M., and Mosteiro M. | title=Insertion Sort is O(n log n) | doi = 10.1007/s00224-005-1237-z }}</ref>

Like the insertion sort it is based on, library sort is a [[stable sort|stable]] [[comparison sort]] and can be run as an [[online algorithm]]; however, it was shown to have a high probability of running in O(n log n) time (comparable to [[quicksortmergesort]]), rather than an insertion sort's O(n²). The mechanism used for this improvement is very similar to that of a [[skip list]]. There is no full implementation given in the paper, nor the exact algorithms of important parts, such as insertion and rebalancing. Further information would be needed to discuss how the efficiency of library sort compares to that of other sorting methods in reality.

Compared to basic insertion sort, the drawback of library sort is that it requires extra space for the gaps. The amount and distribution of that space would be implementation dependent. In the paper the size of the needed array is ''(1 + ε)n'',<ref name="definition" /> but with no further recommendations on how to choose ε.

One weakness of [[insertion sort]] is that it may require a high number of swap operations and be costly if memory write is expensive. Library sort may improve that somewhat in the insertion step, as fewer elements need to move to make room, but is also adding an extra cost in the rebalancing step. In addition, locality of reference will be poor compared to [[mergesort]] as each insertion from a random data set may access memory that is no longer in cache, especially with large data sets.

==Implementation==