On a greedy algorithm to construct universal cycles for permutations

Alice L.L. Gao, Sergey Kitaev, Wolfgang Steiner, Philip B. Zhang

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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 .

Original languageEnglish
Pages (from-to)61-72
Number of pages12
JournalInternational Journal of Foundations of Computer Science
Volume30
Issue number1
DOIs
Publication statusPublished - 5 Mar 2019

Keywords

  • universal cycles
  • permutations
  • greedy algorithm
  • combinatorial generation

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