Abstract
A universal cycle for permutations of length n is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length n, and containing all permutations of length n as factors. It is well known that universal cycles for permutations of length n exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length n, which is based on applying a greedy algorithm to a permutation of length n - 1. We prove that this approach gives a unique universal cycle In for permutations, and we study properties of I n .
| Language | English |
|---|---|
| Pages | 61-72 |
| Number of pages | 12 |
| Journal | International Journal of Foundations of Computer Science |
| Volume | 30 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 5 Mar 2019 |
Keywords
- universal cycles
- permutations
- greedy algorithm
- combinatorial generation
Cite this
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On a greedy algorithm to construct universal cycles for permutations. / Gao, Alice L.L.; Kitaev, Sergey; Steiner, Wolfgang; Zhang, Philip B.
In: International Journal of Foundations of Computer Science, Vol. 30, No. 1, 05.03.2019, p. 61-72.Research output: Contribution to journal › Article
TY - JOUR
T1 - On a greedy algorithm to construct universal cycles for permutations
AU - Gao, Alice L.L.
AU - Kitaev, Sergey
AU - Steiner, Wolfgang
AU - Zhang, Philip B.
PY - 2019/3/5
Y1 - 2019/3/5
N2 - A universal cycle for permutations of length n is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length n, and containing all permutations of length n as factors. It is well known that universal cycles for permutations of length n exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length n, which is based on applying a greedy algorithm to a permutation of length n - 1. We prove that this approach gives a unique universal cycle In for permutations, and we study properties of I n .
AB - A universal cycle for permutations of length n is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length n, and containing all permutations of length n as factors. It is well known that universal cycles for permutations of length n exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length n, which is based on applying a greedy algorithm to a permutation of length n - 1. We prove that this approach gives a unique universal cycle In for permutations, and we study properties of I n .
KW - universal cycles
KW - permutations
KW - greedy algorithm
KW - combinatorial generation
UR - https://arxiv.org/abs/1711.10820
UR - https://www.worldscientific.com/worldscinet/ijfcs
U2 - 10.1142/S0129054119400033
DO - 10.1142/S0129054119400033
M3 - Article
VL - 30
SP - 61
EP - 72
JO - International Journal of Foundations of Computer Science
T2 - International Journal of Foundations of Computer Science
JF - International Journal of Foundations of Computer Science
SN - 0129-0541
IS - 1
ER -