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Article Dans Une Revue European Journal of Combinatorics Année : 2024

The rotation distance of brooms

Jean Cardinal
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Lionel Pournin
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Résumé

The associahedron A(G) of a graph G has the property that its vertices can be thought of as the search trees on G and its edges as the rotations between two search trees. If G is a simple path, then A(G) is the usual associahedron and the search trees on G are binary search trees. Computing distances in the graph of A(G), or equivalently, the rotation distance between two binary search trees, is a major open problem. Here, we consider the different case when G is a complete split graph. In that case, A(G) interpolates between the stellohedron and the permutohedron, and all the search trees on G are brooms. We show that the rotation distance between any two such brooms and therefore the distance between any two vertices in the graph of the associahedron of G can be computed in quasiquadratic time in the number of vertices of G.
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samedi 18 mai 2024
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Dates et versions

hal-04432085 , version 1 (01-02-2024)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

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Jean Cardinal, Lionel Pournin, Mario Valencia-Pabon. The rotation distance of brooms. European Journal of Combinatorics, 2024, 118, pp.103877. ⟨10.1016/j.ejc.2023.103877⟩. ⟨hal-04432085⟩
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