Enumerating homomorphisms

  • Authors:

  • Andrei A. Bulatov;Víctor Dalmau;Martin Grohe;Dániel Marx

  • Affiliations:

  • School of Computing Science, Simon Fraser University, Burnaby, Canada;Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain;Institut für Informatik, Humboldt-Universität, Berlin, Germany;Institut für Informatik, Humboldt-Universität, Berlin, Germany and Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2012

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Abstract

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay.