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arXiv · 1412.4062

Permutation Reconstruction from MinMax-Betweenness Constraints

Irena Rusu
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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.

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Irena Rusu. 2014-12-12. Permutation Reconstruction from MinMax-Betweenness Constraints. https://arxiv.org/abs/1412.4062

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