On a greedy algorithm to construct universal cycles for permutations
Gao, Alice L.L. and Kitaev, Sergey and Steiner, Wolfgang and Zhang, Philip B. (2019) On a greedy algorithm to construct universal cycles for permutations. International Journal of Foundations of Computer Science, 30 (1). pp. 61-72. ISSN 0129-0541 (https://doi.org/10.1142/S0129054119400033)
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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 .
ORCID iDs
Gao, Alice L.L., Kitaev, Sergey ORCID: https://orcid.org/0000-0003-3324-1647, Steiner, Wolfgang and Zhang, Philip B.;-
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Item type: Article ID code: 65203 Dates: DateEvent5 March 2019Published23 January 2019AcceptedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 17 Aug 2018 09:04 Last modified: 02 Sep 2024 17:01 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/65203