An O(n2) time algorithm for the minimal permutation completion problem - Crespelle, Christophe; Perez, Anthony; Todinca, Ioan (Discrete Applied Mathematics, 2019)
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.