Algorithms for junctions in acyclic digraphs

Abstract

Given targets u and v in a digraph D, we say that a vertex s is a junction of u and v if there are in D internally vertex-disjoint directed paths from s to u and from s to v. In this paper, we show how to characterize junctions in acyclic digraphs. We also consider the following problem and derive an efficient algorithm to solve it. Given an acyclic digraph D, a vertex s in D and k pairs of targets {u 1,v 1},⋯,{u k,v k }, determine the pairs of targets {u i,v i } for which s is a junction. This problem arises in an application brought to our attention by an anthropologist. In this application the digraph represents the genealogy of an ethnic group in Brazilian Amazon region, and the pairs of targets are individuals that are married. We apply our algorithm to find all the junctions of k pairs of targets on those kinship networks. Experiments have shown that our algorithm had a good performance for the inputs considered. Some results are described in this paper.