Permutation Reconstruction from MinMax-Betweenness Constraints
Year: 2014
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Rusu, Irena
Institutions: Université de Nantes, Nantes Université
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951511609