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Article Dans Une Revue International Journal of Foundations of Computer Science Année : 2019

On a Greedy Algorithm to Construct Universal Cycles for Permutations

Résumé

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 $\Pi_n$ for permutations, and we study properties of $\Pi_n$.

Dates et versions

hal-02348031 , version 1 (05-11-2019)

Identifiants

Citer

Alice L. L. Gao, Sergey Kitaev, Wolfgang Steiner, Philip B. Zhang. On a Greedy Algorithm to Construct Universal Cycles for Permutations. International Journal of Foundations of Computer Science, 2019, 30 (01), pp.61-72. ⟨10.1142/S0129054119400033⟩. ⟨hal-02348031⟩
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