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2018 ; 34
(13
): i313-i322
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Enumerating consistent sub-graphs of directed acyclic graphs: an insight into
biomedical ontologies
#MMPMID29949985
Peng Y
; Jiang Y
; Radivojac P
Bioinformatics
2018[Jul]; 34
(13
): i313-i322
PMID29949985
show ga
MOTIVATION: Modern problems of concept annotation associate an object of interest
(gene, individual, text document) with a set of interrelated textual descriptors
(functions, diseases, topics), often organized in concept hierarchies or
ontologies. Most ontology can be seen as directed acyclic graphs (DAGs), where
nodes represent concepts and edges represent relational ties between these
concepts. Given an ontology graph, each object can only be annotated by a
consistent sub-graph; that is, a sub-graph such that if an object is annotated by
a particular concept, it must also be annotated by all other concepts that
generalize it. Ontologies therefore provide a compact representation of a large
space of possible consistent sub-graphs; however, until now we have not been
aware of a practical algorithm that can enumerate such annotation spaces for a
given ontology. RESULTS: We propose an algorithm for enumerating consistent
sub-graphs of DAGs. The algorithm recursively partitions the graph into strictly
smaller graphs until the resulting graph becomes a rooted tree (forest), for
which a linear-time solution is computed. It then combines the tallies from
graphs created in the recursion to obtain the final count. We prove the
correctness of this algorithm, propose several practical accelerations, evaluate
it on random graphs and then apply it to characterize four major biomedical
ontologies. We believe this work provides valuable insights into the complexity
of concept annotation spaces and its potential influence on the predictability of
ontological annotation. AVAILABILITY AND IMPLEMENTATION:
https://github.com/shawn-peng/counting-consistent-sub-DAG. SUPPLEMENTARY
INFORMATION: Supplementary data are available at Bioinformatics online.