Section: Overall Objectives

Highlight 2011 on the Subgraph Epimorphism Problem

The subgraph epimorphism (SEPI) problem is a variant of graph matching problem. Our interest in SEPIs 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. We have shown last year that in this setting, the notion of model reduction can be formalized as the existence of a sequence of vertex deletion and merge operations that 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.

This year we have shown that the SEPI existence problem between two graphs is NP-complete by reduction of the set covering problem [5] and on the algorithmic side, we provide a constraint satisfaction algorithm [10] that has been successfully used to solve SEPI matching problems on a large benchmark of reaction graphs extracted from the repository of systems biology models biomodels.net . In [5] , we develop the theory of subgraph epimorphisms in general directed graphs. First, subgraph epimorphisms (SEPI), subgraph isomorphisms (SISO) and graph epimorphisms (EPI) are characterized in terms of graph transformation operations. Then the graph distance measures induced by these transformations are compared and shown to define metrics on graphs.