An O(n2) time algorithm for the minimal permutation completion problem

In the Minimal Permutation Completion problem, one is given an arbitrary graph G=(V,E) and the aim is to find a permutation super-graph H=(V,F) defined on the same vertex set and such that F⊇E is inclusion-minimal among all possibilities. The graph H is then called a minimal permutation completion o...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 254; pp. 80 - 95
Main Authors Crespelle, Christophe, Perez, Anthony, Todinca, Ioan
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.02.2019
Elsevier BV
Elsevier
Subjects
Algorithms
Computer Science
Data Structures and Algorithms
Minimal permutation completion
Permutation graph
Permutations
Polynomial algorithm
Polynomials
Polynomial algorithm
Minimal permutation completion
Permutation graph
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ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2018.06.036

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Summary:In the Minimal Permutation Completion problem, one is given an arbitrary graph G=(V,E) and the aim is to find a permutation super-graph H=(V,F) defined on the same vertex set and such that F⊇E is inclusion-minimal among all possibilities. The graph H is then called a minimal permutation completion of G. We provide an O(n2) incremental algorithm computing such a minimal permutation completion. To the best of our knowledge, this result leads to the first polynomial algorithm for this problem. A preliminary extended abstract of this paper appeared as [4] in the Proceedings of WG 2015.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.06.036