Image retrieval by spatial arrangement underlies a matching algorithm, which ``interprets'' entities specified in the user query on the entities appearing in the image of the database, and which jointly compares their features and their spatial relationships.In this paper, we provide a graph-theoretical formulation and we discuss the size for the problem of spatial matching as encountered in the specific application context of retrieval by visual content. We then expound and evaluate three state-space search algorithms which support efficient comparison of models through a heuristic bounding approach.