Section: New Results

Structural Model Reduction: CLP and SAT Solvers for Computing Subgraph Epimorphisms

Participants : François Fages, Steven Gay, Thierry Martinez, Francesco Santini, Sylvain Soliman.

This year, in [8] , we have developed and compared 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 vertices, species or reaction, deletion and merge operations which transforms a first reaction graph into a second graph (Steven Gay, Sylvain Soliman, François Fages. A Graphical Method for Reducing and Relating Models in Systems Biology. Bioinformatics, 26(18):i575–i581, 2010.). 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.