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. 
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45 Citations
Highly Influential Citations
6
Background Citations
13
Methods Citations
12
Results Citations
1

45 Citations

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.
New recursive circular algorithm for listing all permutations
TLDR
A new recursive strategy is proposed to generate starter sets that will not incur equivalence by circular operation and the result indicates that the new algorithm is faster than the other two in time execution.
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…
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.
Star transposition Gray codes for multiset permutations
TLDR
The proofs establish Hamilton-connectedness or Hamilton-laceability of the underlying flip graphs, and they answer several cases of a recent conjecture of Shen and Williams.
Parallel Algorithm for Generating Permutations on Linear Array
The Greedy Gray Code Algorithm
We reinterpret classic Gray codes for binary strings, permutations, combinations, binary trees, and set partitions using a simple greedy algorithm. The algorithm begins with an initial object and an…
On The Diameter of Pancake Graphs
The Pancake graph( P n ) represents the group of all permutations on n elements, namely S n , with respect to the generating set containing all prefix reversals. The diameter of a graph is the maximum…
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References

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