Publication Details |
| Category | Text Publication |
| Reference Category | Journals |
| DOI | 10.1016/j.dam.2021.12.017 |
| Licence |
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| Title (Primary) | From modular decomposition trees to rooted median graphs |
| Author | Bruckmann, C.; Stadler, P.F.; Hellmuth, M. |
| Journal | Discrete Applied Mathematics |
| Year | 2022 |
| Department | UMB |
| Volume | 310 |
| Page From | 1 |
| Page To | 9 |
| Language | englisch |
| Topic | T7 Bioeconomy |
| Keywords | 2-structures; Symbolic ultrametrics; Modular decomposition; Prime module; Prime vertex replacement; Median graph; Algorithm; Half-grid; Hypercube |
| Abstract | The modular decomposition of a symmetric map delta:X x X -> Upsilon (or, equivalently, a set of pairwise-disjoint symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of delta in terms of a labeled tree. A map delta is explained by a vertex-labeled rooted tree (T, t) if the label delta(x, y) coincides with the label of the lowest common ancestor of x and y in T, i.e., if delta(x, y) = t(lca(x, y)). Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be explained in this manner. Here we consider rooted median graphs as a generalization of (modular decomposition) trees to explain symmetric maps. We derive a linear-time algorithm that stepwisely resolves prime vertices in the modular decomposition tree to obtain a rooted and labeled median graph that explains a given symmetric map delta. |
| Persistent UFZ Identifier | https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=26884 |
| Bruckmann, C., Stadler, P.F., Hellmuth, M. (2022): From modular decomposition trees to rooted median graphs Discrete Appl. Math. 310 , 1 - 9 |
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