Library sort

Library sort, or gapped insertion sort is a sorting algorithm that uses an insertion sort, but with gaps in the array to accelerate subsequent insertions. The name comes from an analogy:

The algorithm was proposed by Michael A. Bender, Martín Farach-Colton, and Miguel Mosteiro in 2004 and was published in 2006.

Like the insertion sort it is based on, library sort is a 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 quicksort), 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, but with no further recommendations on how to choose ε.