Corpus ID: 57573655

An in-place, subquadratic algorithm for permutation inversion

@article{Guspiel2019AnIS,
  title={An in-place, subquadratic algorithm for permutation inversion},
  author={Grzegorz Guspiel},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.01926}
}
We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time with a simple algorithm. Limiting the numbers that can be stored in our array to the range $[1...n]$ still allows a straightforward $O(n^2)$ time solution. The time complexity can be improved using randomization, but this only improves the expected, not the… Expand
Strictly In-Place Algorithms for Permuting and Inverting Permutations
TLDR
A strictly in-place algorithm for inverting a given permutation on n elements working in the same complexity is obtained, a significant improvement on a recent result of Guśpiel [arXiv 2019], who designed an O(n)-time algorithm. Expand

References

SHOWING 1-9 OF 9 REFERENCES
Permuting in Place
TLDR
The goal is to perform the permutation quickly using only a polylogarithmic number of bits of extra storage, and the main result is an algorithm whose worst case running time is $O(n \log n)$ and that uses additional $\log n-bit words of memory. Expand
Inverting Permutations In Place
In this thesis, we address the problem of quickly inverting the standard representation of a permutation on n elements in place. First, we present a naive algorithm to do it using O(log n) extra bitsExpand
The art of computer programming. Vol.2: Seminumerical algorithms
TLDR
This professional art of computer programming volume 2 seminumerical algorithms 3rd edition that has actually been written by is one of the best seller books in the world and is never late to read. Expand
An improved Monte Carlo factorization algorithm
TLDR
A cycle-finding algorithm is described which is about 36 percent faster than Floyd's (on the average), and applied to give a Monte Carlo factorization algorithm which is similar to Pollard's but about 24 percent faster. Expand
The Art in Computer Programming
TLDR
Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on. Expand
The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition
A container closure assembly for maintaining a sterile sealed container is provided having a ferrule having a top annular portion and a depending skirt portion for securing a resilient stopper forExpand
The Art of Computer Programming, Volume 1 (3rd Ed.)
  • Fundamental Algorithms. Addison Wesley Longman Publishing Co., Inc.,
  • 1997
The Art of Computer Programming, Volume 2 (3rd Ed.)
  • Seminumerical Algorithms. Addison Wesley Longman Publishing Co., Inc.,
  • 1997
, and Patricio V . Poblete . Permuting in place
  • SIAM J . Comput .
  • 1995