Corrigendum to “Best match graphs”

Schaller, David; Geiß, Manuela; Chávez, Edgar; Laffitte, Marcos González; Sánchez, Alitzel López; Stadler, Bärbel M. R.; Valdivia, Dulce I.; Hellmuth, Marc; Hernández-Rosales, Maribel; Stadler, Peter F.

doi:10.1007/s00285-021-01601-6

Cited by 11 publications

(11 citation statements)

References 5 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [3,4,5], BMGs have been characterized in terms of certain sets of rooted triples that easily can be constructed for every given vertex-colored digraph: For vertex-colored digraphs that are associated with binary trees, we will furthermore need…”

Section: Best Match Graphsmentioning

confidence: 99%

“…Best match graphs then collect the best match information for a family of related genes from different species. Because of their close connection to the practically important problem of orthology detection, which often starts from reciprocal best matches, BMGs have been studied in some detail [1,2,3,4,5]. Two-colored BMGs, furthermore, are characterized by four properties of the out-neighborhoods of its vertices.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quasi-Best Match Graphs

Korchmaros¹,

Schaller²,

Hellmuth³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Quasi-best match graphs (qBMGs) are a hereditary class of directed, properly vertex-colored graphs. They arise naturally in mathematical phylogenetics as a generalization of best match graphs, which formalize the notion of evolutionary closest relatedness of genes (vertices) in multiple species (vertex colors). They are explained by rooted trees whose leaves correspond to vertices. In contrast to BMGs, qBMGs represent only best matches at a restricted phylogenetic distance. We provide characterizations of qBMGs that give rise to polynomial-time recognition algorithms and identify the BMGs as the qBMGs that are color-sink-free. Furthermore, two-colored qBMGs are characterized as directed graphs satisfying three simple local conditions, two of which have appeared previously, namely bi-transitivity in the sense of Das et al. (2021) and a hierarchy-like structure of out-neighborhoods, i.e., N (x) ∩ N (y) ∈ {N (x), N (y), ∅} for any two vertices x and y. Further results characterize qBMGs that can be explained by binary phylogenetic trees.

show abstract

Section: Best Match Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasi-Best Match Graphs

Korchmaros¹,

Schaller²,

Hellmuth³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a recent work, we have shown that such trees can be inferred e.g. as the least resolved trees from best match data [ 9 , 10 ] and from information of horizontal gene transfer [ 11 , 12 ]. Denoting with the set of “clusters” in T , we recently showed that the latter type of data can be explained by a common evolutionary scenario if and only if (1) both the best match and the horizontal transfer data can be explained by least resolved trees and , respectively, and (2) the union is again a hierarchy.…”

Section: Introductionmentioning

confidence: 99%

A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

Schaller

Hellmuth

Stadler

2021

Algorithms Mol Biol

Self Cite

View full text Add to dashboard Cite

Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

show abstract

“…Defs. 1 and 2 below), form a very restrictive class of colored digraphs [6,7]. Empirically determined best hit data therefore will in general not satisfy the defining properties of BMGs.…”

Section: Introductionmentioning

confidence: 99%

“…A formal definition of triple consistency will be provided in the next section. In [7], it was shown that a vertex-colored digraph ( � G = (V , E), σ ) is a BMG if and only if (a) the set of informative triples R( G, σ ) is consistent and (b) the BMG � G(T , σ ) of the corresponding so-called Aho tree T := Aho (R( � G, σ ), V ) coincides with ( G, σ ) . In general, the Aho tree Aho (R, V ) of a consistent set of triples R on a set V is a least resolved supertree of all the triples in R .…”

Section: Introductionmentioning

confidence: 99%

Heuristic algorithms for best match graph editing

Schaller

Geiß

Hellmuth

et al. 2021

Algorithms Mol Biol

Self Cite

View full text Add to dashboard Cite

Background Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics as a representation of the pairwise most closely related genes among multiple species. An arc connects a gene x with a gene y from another species (vertex color) Y whenever it is one of the phylogenetically closest relatives of x. BMGs can be approximated with the help of similarity measures between gene sequences, albeit not without errors. Empirical estimates thus will usually violate the theoretical properties of BMGs. The corresponding graph editing problem can be used to guide error correction for best match data. Since the arc set modification problems for BMGs are NP-complete, efficient heuristics are needed if BMGs are to be used for the practical analysis of biological sequence data. Results Since BMGs have a characterization in terms of consistency of a certain set of rooted triples (binary trees on three vertices) defined on the set of genes, we consider heuristics that operate on triple sets. As an alternative, we show that there is a close connection to a set partitioning problem that leads to a class of top-down recursive algorithms that are similar to Aho’s supertree algorithm and give rise to BMG editing algorithms that are consistent in the sense that they leave BMGs invariant. Extensive benchmarking shows that community detection algorithms for the partitioning steps perform best for BMG editing. Conclusion Noisy BMG data can be corrected with sufficient accuracy and efficiency to make BMGs an attractive alternative to classical phylogenetic methods.

show abstract

Corrigendum to “Best match graphs”

Cited by 11 publications

References 5 publications

Quasi-Best Match Graphs

Quasi-Best Match Graphs

A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

Heuristic algorithms for best match graph editing

Contact Info

Product

Resources

About