Algorithms for Junctions in Directed Acyclic Graphs

TL;DR

This paper characterizes junctions in directed acyclic graphs and develops efficient algorithms to identify all junctions for given vertex pairs, with applications in anthropology and kinship network analysis.

Contribution

It introduces a characterization of junctions in DAGs and provides algorithms for finding and preprocessing junctions for multiple vertex pairs.

Findings

Efficient algorithms for identifying junctions in DAGs.

Application of algorithms to kinship networks of Brazilian indigenous groups.

Demonstrated practical utility in anthropology research.

Abstract

Given a pair of distinct vertices u, v in a graph G, we say that s is a junction of u, v if there are in G internally vertex disjoint directed paths from s to u and from s to v. We show how to characterize junctions in directed acyclic graphs. We also consider the two problems in the following and derive efficient algorithms to solve them. Given a directed acyclic graph G and a vertex s in G, how can we find all pairs of vertices of G such that s is a junction of them? And given a directed acyclic graph G and k pairs of vertices of G, how can we preprocess G such that all junctions of k given pairs of vertices could be listed quickly? All junctions of k pairs problem arises in an application in Anthropology and we apply our algorithm to find such junctions on kinship networks of some brazilian indian ethnic groups.