The main research in the area of image databases addresses the improvement of retrieval quality and the speedup of the query processing. A number of image retrieval systems reached meanwhile a level, where these are used in real-world applications and thus create new demands. In particular dealing with a large, simultaneous number of users and queries requires concepts for resource management, which strongly consider the underlying architecture and the various approaches for image retrieval. This paper is our first step in this direction, as it provides a formal problem specification and a proof that this problem is NP-hard.