Permutation reconstruction from MinMax-Betweenness constraints

In this paper, we investigate the reconstruction of permutations on {1,2,…,n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1,2,…,n−1. We propose two variants of the problem (directed and undirected), and focus first on the directed v...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 207; pp. 106 - 119
Main Author Rusu, Irena
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.07.2016
Elsevier
Subjects
Algorithm
Betweenness constraints
Computational Complexity
Computer Science
Permutation reconstruction
Algorithm
Betweenness constraints
Permutation reconstruction
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Summary:In this paper, we investigate the reconstruction of permutations on {1,2,…,n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1,2,…,n−1. We propose two variants of the problem (directed and undirected), and focus first on the directed version, for which we draw up general features and design a polynomial algorithm in a particular case. Then, we investigate necessary and sufficient conditions for the uniqueness of the reconstruction in both directed and undirected versions, using a parameter k whose variation controls the stringency of the betweenness constraints. We finally point out open problems.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.03.008