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Algorithms for Junctions in Acyclic Digraphs

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Facets of Combinatorial Optimization

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.

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Acknowledgements

C.E. Ferreira is supported by CNPq (Proc. 302736/10-7 and 477203/12-4). A.J.P. Franco is supported by CAPES (Proc. 33002010176P0). We want to thank Professor Marcio Ferreira da Silva (Anthropology Department, University of São Paulo) who brought this problem (and other related to kinship networks) to our attention and provided us the data used in these experiments. We also thank the anonymous referees for their constructive comments.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Rua do Matão, 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil

    Carlos Eduardo Ferreira & Álvaro Junio Pereira Franco

Authors
  1. Carlos Eduardo Ferreira
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  2. Álvaro Junio Pereira Franco
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Correspondence to Carlos Eduardo Ferreira .

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Editors and Affiliations

  1. Dept. of Computer Science, University of Cologne, Pohligstr. 1, Cologne, 50969, Germany

    Michael Jünger

  2. Dept. of Computer Science, University of Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany

    Gerhard Reinelt

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Ferreira, C.E., Franco, Á.J.P. (2013). Algorithms for Junctions in Acyclic Digraphs. In: Jünger, M., Reinelt, G. (eds) Facets of Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38189-8_8

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