
An
Efficient
Generalization
of
Counting
Sort
for
Large,
possibly
Infinite
Key
Ranges
Title: 
An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges 
Author:

Pasquale Noce (pasquale /dot/ noce /dot/ lavoro /at/ gmail /dot/ com)

Submission date: 
20191204 
Abstract: 
Counting sort is a wellknown algorithm that sorts objects of any kind
mapped to integer keys, or else to keys in onetoone correspondence
with some subset of the integers (e.g. alphabet letters). However, it
is suitable for direct use, viz. not just as a subroutine of another
sorting algorithm (e.g. radix sort), only if the key range is not
significantly larger than the number of the objects to be sorted.
This paper describes a tailrecursive generalization of counting sort
making use of a bounded number of counters, suitable for direct use in
case of a large, or even infinite key range of any kind, subject to
the only constraint of being a subset of an arbitrary linear order.
After performing a penandpaper analysis of how such algorithm has to
be designed to maximize its efficiency, this paper formalizes the
resulting generalized counting sort (GCsort) algorithm and then
formally proves its correctness properties, namely that (a) the
counters' number is maximized never exceeding the fixed upper
bound, (b) objects are conserved, (c) objects get sorted, and (d) the
algorithm is stable. 
BibTeX: 
@article{Generalized_Counting_SortAFP,
author = {Pasquale Noce},
title = {An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges},
journal = {Archive of Formal Proofs},
month = dec,
year = 2019,
note = {\url{http://isaafp.org/entries/Generalized_Counting_Sort.html},
Formal proof development},
ISSN = {2150914x},
}

License: 
BSD License 
