Enumerating Homomorphisms

Authors Andrei A. Bulatov, Victor Dalmau, Martin Grohe, Daniel Marx

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Andrei A. Bulatov
Victor Dalmau
Martin Grohe
Daniel Marx

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Andrei A. Bulatov, Victor Dalmau, Martin Grohe, and Daniel Marx. Enumerating Homomorphisms. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 231-242, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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.


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