| Sorting multisets stably in minimum space | |
| Authors: | Jyrki Katajainen and Tomi Pasanen |
| Published in: | Proceedings of the 3rd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science 621, Springer-Verlag (1992), 410-421 |
| DOI: | 10.1007/3-540-55706-7_37 |
| Copyright: | © Springer-Verlag |
| Abstract: | In a decision tree model, Ω(nlog2n − ∑i=1m nilog2ni+n) is known to be a lower bound for sorting a multiset of size n containing m distinct elements, where the ith distinct element appears ni times. We present a minimum space algorithm that sorts stably a multiset in asymptotically optimal worst-case time. A Quicksort type approach is used, where at each recursive step the median is chosen as the partitioning element. To obtain a stable minimum space implemention, we develop linear-time in-place algorithms for the following problems, which have interest of their own: Stable unpartitioning: Assume that an n-element array A is stably partitioned into two subarrays A0 and A1. The problem is to recover A from its constituents A0 and A1. The information available is the partitioning element used and a bit array of size n indicating whether an element of A0 or A1 was originally in the corresponding position of A. Stable selection: The task is to find the kth smallest element in a multiset of n elements such that the relative order of identical elements is retained. |
| Related: |  HTML (Journal article) |
| BibLATEX: | @inproceedings{KP1992dC,
author = {Jyrki Katajainen and Tomi Pasanen},
title = {Sorting multisets stably in minimum space},
booktitle = {Proceedings of the 3rd Scandinavian Workshop on Algorithm
Theory},
series = {Lecture Notes in Computer Science},
volume = {621},
publisher = {Springer-Verlag},
year = {1992},
pages = {410--421},
}
|