The paper formulates and investigates the aggregation problem for synthesized mediators of Web services (SWMs). An SWM is a finite-state transducer defined in terms of templates for component services. Upon receiving an artifact, an SWM selects a set of available services from a library to realize its templates, and invokes those services to operate on the artifact, in parallel; it produces a numeric value as output (e.g., the total price of a package) by applying synthesis rules. Given an SWM, a library and an input artifact, the aggregation problem is to find a mapping from the component templates of the SWM to available services in the library that maximizes (or minimizes) the output. As opposed to the composition syntheses of Web services, the aggregation problem aims to optimize the realization of a given mediator, to best serve the users’ need. We analyze this problem, and show that its complexity depends on the underlying graph structure of the mediator: while it is undeci...