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An Algorithmic Framework for Locally Constrained Homomorphisms

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Graph-Theoretic Concepts in Computer Science (WG 2022)

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Abstract

A homomorphism \(\phi \) from a guest graph G to a host graph H is locally bijective, injective or surjective if for every \(u\in V(G)\), the restriction of \(\phi \) to the neighbourhood of u is bijective, injective or surjective, respectively. The corresponding decision problems, LBHom, LIHom and LSHom, are well studied both on general graphs and on special graph classes. We prove a number of new \(\textsf{FPT}\), \(\textsf{W}\)[1]-hard and para-\(\textsf{NP}\)-complete results by considering a hierarchy of parameters of the guest graph G. For our \(\textsf{FPT}\) results, we do this through the development of a new algorithmic framework that involves a general ILP model. To illustrate the applicability of the new framework, we also use it to prove \(\textsf{FPT}\) results for the Role Assignment problem, which originates from social network theory and is closely related to locally surjective homomorphisms.

The second and fourth authors acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC, project EP/V00252X/1).

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Author information

Authors and Affiliations

  1. LIGM, CNRS, Université Gustave Eiffel, Champs-sur-Marne, France

    Laurent Bulteau

  2. School of Computing, Newcastle University, Newcastle upon Tyne, UK

    Konrad K. Dabrowski

  3. LAMSADE, CNRS, Université Paris-Dauphine, PSL University, Paris, France

    Noleen Köhler

  4. School of Computing, University of Leeds, Leeds, UK

    Sebastian Ordyniak

  5. Department of Computer Science, University of Durham, Durham, UK

    Daniël Paulusma

Authors
  1. Laurent Bulteau
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  2. Konrad K. Dabrowski
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  3. Noleen Köhler
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  4. Sebastian Ordyniak
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  5. Daniël Paulusma
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Corresponding author

Correspondence to Konrad K. Dabrowski .

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Editors and Affiliations

  1. University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Universität Tübingen, Tübingen, Germany

    Michael Kaufmann

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Bulteau, L., Dabrowski, K.K., Köhler, N., Ordyniak, S., Paulusma, D. (2022). An Algorithmic Framework for Locally Constrained Homomorphisms. In: Bekos, M.A., Kaufmann, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2022. Lecture Notes in Computer Science, vol 13453. Springer, Cham. https://doi.org/10.1007/978-3-031-15914-5_9

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