Solving Subgraph Epimorphism Problems using CLP and SAT

Abstract : In this work, we compare CLP and SAT solvers on the NP-complete problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex, species or reaction, deletion and merge operations which transforms a first reaction graph into a second graph. This problem is in turn equivalent to the existence of a subgraph (corresponding to delete operations) epimorphism (i.e. surjective homomorphism, corresponding to merge operations) from the first graph to the second. We show how subgraph epimorphism problems can be modeled as Boolean constraint satisfaction problems, and we compare CLP and SAT solvers on a large benchmark of reaction graphs from systems biology.
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Steven Gay, François Fages, Francesco Santini, Sylvain Soliman. Solving Subgraph Epimorphism Problems using CLP and SAT. WCB - ninth Workshop on Constraint Based Methods for Bioinformatics, colocated with CP 2013 (2013), Sep 2013, Uppsala, Sweden. pp.67--74. ⟨hal-00908973⟩

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