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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| Published in | Discrete Applied Mathematics Vol. 254; pp. 80 - 95 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
15.02.2019
Elsevier BV Elsevier |
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| ISSN | 0166-218X 1872-6771 |
| DOI | 10.1016/j.dam.2018.06.036 |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Crespelle, Christophe Perez, Anthony Todinca, Ioan |
| Author_xml | – sequence: 1 givenname: Christophe surname: Crespelle fullname: Crespelle, Christophe email: christophe.crespelle@inria.fr organization: Université Claude Bernard Lyon 1 and CNRS, DANTE/INRIA, LIP UMR CNRS 5668, ENS de Lyon, Université de Lyon, France – sequence: 2 givenname: Anthony surname: Perez fullname: Perez, Anthony email: anthony.perez@univ-orleans.fr organization: Univ. Orléans, INSA Centre Val de Loire, LIFO EA 4022, FR-45067 Orléans, France – sequence: 3 givenname: Ioan surname: Todinca fullname: Todinca, Ioan email: ioan.todinca@univ-orleans.fr organization: Univ. Orléans, INSA Centre Val de Loire, LIFO EA 4022, FR-45067 Orléans, France |
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| Cites_doi | 10.1016/j.disc.2005.12.003 10.1137/0205021 10.1007/BF02022041 10.1016/j.tcs.2012.12.031 10.1016/j.ipl.2007.11.013 10.1016/j.dam.2006.03.031 10.1016/j.dam.2009.01.016 10.1137/S0895480104445010 10.1137/0602010 10.1016/j.dam.2007.08.039 10.1016/j.dam.2008.08.010 10.1137/0205012 10.1016/0022-0000(81)90022-2 10.1007/s00453-008-9273-0 |
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| Keywords | Polynomial algorithm Minimal permutation completion Permutation graph |
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| Snippet | 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... 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... |
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| SubjectTerms | Algorithms Computer Science Data Structures and Algorithms Minimal permutation completion Permutation graph Permutations Polynomial algorithm Polynomials |
| Title | An O(n2) time algorithm for the minimal permutation completion problem |
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