Nearly All Reals Can Be Sorted with Linear Time Complexity

0544787 - ÚI 2022 CZ eng V - Výzkumná zpráva
Jiřina, Marcel
Nearly All Reals Can Be Sorted with Linear Time Complexity.
Prague: ICS CAS, 2021. 22 s. Technical Report, V-1285.
Grant CEP: GA MŠMT LM2015068
Institucionální podpora: RVO:67985807
Klíčová slova: sorting * algorithm * real sorting key * time complexity * linear complexity

We propose a variant of the counting sort modified for sorting reals in a linear time. It is assumed that the sorting key and pointers to the items being sorted are moved and individual items remain at the same place in the memory (in place sorting). In this case, the space complexity of the new variant of the algorithm is the same as the complexity of the quicksort. We also quantify the practical limits for possible sorting reals in a linear time. This possibility is assured under additional assumptions on the distribution of the sorting key, mainly the independence and identity of the distribution. Here we give a more general criteria easily applicable in practice. We also show that the algorithm is applicable for data that do not fulfill criteria for linear time complexity but even that the computation is faster than the system quicksort. A new, faster version of the algorithm is attached.
Trvalý link: http://hdl.handle.net/11104/0321594