An · algorithm for calculating the closure of lca-type operators
نویسندگان
چکیده
The least common ancestor on two vertices, denoted , , is a well defined operation in a directed acyclic graph (dag) . We introduce , a natural extension of , for any set of vertices. Given such a set , one can iterate in order to obtain an increasing set sequence. being finite, this sequence has always a limit which defines a closure operator. Two equivalent definitions of this operator are given and their relationships with abstract convexity are shown. The good properties of this operator permit to conceive an · time complexity algorithm to calculate its closure. This performance is crucial in applications where dags of thousands of vertices are employed. Two examples are given in the domain of life-science: the first one concerns genes annotations understanding by restricting Gene Ontology, the second one deals with identifying taxonomic group of environmental DNA sequences. Keywords—Directed acyclic graph, Least common ancestor, Greatest common descendant, Closure operator, Abstract Convexity.
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