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- Bruckmann, Carmen, et al.
(author)
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From modular decomposition trees to rooted median graphs
- 2022
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In: Discrete Applied Mathematics. - : Elsevier BV. - 0166-218X .- 1872-6771. ; 310, s. 1-9
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Journal article (peer-reviewed)abstract
- The modular decomposition of a symmetric map δ:X×X→Υ (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 δ in terms of a labeled tree. A map δ is explained by a vertex-labeled rooted tree (T,t) if the label δ(x,y) coincides with the label of the lowest common ancestor of x and y in T, i.e., if δ(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 δ.
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