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On the Complexity of Directed Intersection Representation of DAGs

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Computing and Combinatorics (COCOON 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12273))

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Abstract

Motivated by the study of networks of web-pages generated by their information content, Kostochka et al. [ISIT 2019] introduced a novel notion of directed intersection representation of a (acyclic) directed graph and studied the problem of determining the directed intersection number of a digraph D,  henceforth denoted by DIN(D),  defined as the minimum cardinality of a ground set \(\mathcal{C}\) such that it is possible to assign to each vertex \(v \in V(D)\) a subset \(\varphi (v) \in \mathcal{C}\) such that \((u,v) \in E(D)\) if and only if the following two conditions hold: (i) \(\varphi (v) \cap \varphi (u) \ne \emptyset \); (ii) \(|\varphi (u)| < |\varphi (v)|\).

In this paper we show that determining DIN(D) is NP-hard. We also show a 2-approximation algorithm for arborescences.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Andrea Caucchiolo & Ferdinando Cicalese

Authors
  1. Andrea Caucchiolo
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  2. Ferdinando Cicalese
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Corresponding author

Correspondence to Ferdinando Cicalese .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, USA

    Donghyun Kim

  2. Department of Mathematics and Physics, North Carolina Central University, Durham, NC, USA

    R. N. Uma

  3. Computer Science, Georgia State University, Atlanta, GA, USA

    Zhipeng Cai

  4. Korea University, Seoul, Korea (Republic of)

    Dong Hoon Lee

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Caucchiolo, A., Cicalese, F. (2020). On the Complexity of Directed Intersection Representation of DAGs. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_45

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  • DOI: https://doi.org/10.1007/978-3-030-58150-3_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58149-7

  • Online ISBN: 978-3-030-58150-3

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