A new algorithm for generation of permutations

@article{Zaks1984ANA,
  title={A new algorithm for generation of permutations},
  author={Shmuel Zaks},
  journal={BIT Numerical Mathematics},
  year={1984},
  volume={24},
  pages={196-204}
}
  • S. Zaks
  • Published 1 June 1984
  • Mathematics, Computer Science
  • BIT Numerical Mathematics
A new algorithm for generating permutations is presented, that generates the next permutation by reversing a certain suffix of its predecessor. The average size of this suffix is less thane ≅ 2.8. It is shown how to find the position of a given permutation and how to construct the permutation of a given position, where the position refers to the order in which the permutations are generated, and is also new. 
View on Springer
wikidata.org
45 Citations
Highly Influential Citations
6
Background Citations
13
Methods Citations
12
Results Citations
1

45 Citations

Parallel permutation generation on linear array
  • Chau-Jy Lin
  • Mathematics, Computer Science
    Int. J. Comput. Math.
  • 1991
TLDR
A parallel algorithm for generating all the n! permutations is presented and the basic idea used is the iterative method and the exchange of two consecutive components in an existing permutation.
Parallel generation of permutations and combinations
TLDR
A parallel algorithm to generate the permutations of at mostk out ofn objects which achieves the best possible speedup for any givenk and can be modified to generate combinations.
On generation of permutations through decomposition of symmetric groups into cosets
A hardware-oriented algorithm for generating permutations is presented that takes as a theoretic base an iterative decomposition of the symmetric groupSn into cosets. It generates permutations in a…
A Unified Framework to Discover Permutation Generation Algorithms
TLDR
Two simple, intuitive, and general algorithmic frameworks can be used to design a wide variety of permutation generation algorithms, including the well-known algorithms of Heap, Wells, Langdon, Zaks, Tompkins, and Lipski.
Efficient enumeration of cyclic permutations in situ
  • M. Er
  • Computer Science, Mathematics
  • 1989
TLDR
An efficient algorithm for generating all cyclic permutations of length n is derived, and its correctness is proven.
On Generation of Permutations through Suffix/Prefix Reversing in a Cellular Network
In this paper a new permutation generator is proposed. Each subsequent permutation is generated in a cellular permutation network by reversing a suffix/prefix of the preceding permutation. The…
Parallel generation of permutations on systolic arrays
New Permutation Generation Under Exchange Strategy (PGuES)
TLDR
An exchange based technique for generating permutation that involved exchanging two consecutive elements, to generate the starter sets and the numerical result shows that new method is better than other existing methods.
Application of half butterfly method in listing permutation
TLDR
This paper presented a permutation generation using Half Butterfly Method, a new method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism.
On generation of permutations through su x / pre x reversing in a cellular network
In this paper a new permutation generation algorithm is proposed. Each subsequent permutation is generated in a cellular permutation network by reversing a su x/pre x of the preceding permutation.…
...
...

References

SHOWING 1-8 OF 8 REFERENCES
A simplified loop-free algorithm for generating permutations
TLDR
A simplification of Ehrlich's loop-free version of Johnson and Trotter's algorithm for generation of all permutations of a set of elements and its validity is proved.
Bounds for sorting by prefix reversal
Permutation Generation Methods
TLDR
The paper is intended not only as a survey of permuta t ion generation methods, but also as a tutomal on how to compare a number of different algori thms for the same task.
Generation of permutations by adjacent transposition
1. RICHARD S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Inc., 1962. 2. E. G. D'YAKONOV, "On a Method of Solving the Poisson Equation," Dokl. Akad. Nauk SSSR 143 (1962), 21-24, the same paper…
Algorithm 115: Perm
this cyclic o r d e r-t h e vertices of a simple closed p o l y g o n a n d (x0, y0) is a p o i n t n o t on a n y side of t h e polygon, t h e n t h e procedure d e t e r m i n e s , b y s e t t i n…
Combinatorial algorithms
Loopless Algorithms for Generating Permutations, Combinations, and Other Combinatorial Configurations
The purpose of this work is to find a method for building loopless algorithms for listing combinatorial items, like partitions, permutations, combinations. Gray code, etc. Algorithms for the above…
Algorithm 466: four combinatorial algorithm [G6]