Constraint-driven Communication Synthesis enables the automatic design of the communication architecture of a complex system from a library of pre-defined Intellectual Property (IP) components. The key communication parameters that govern all the point-to-point interactions among system modules are captured as a set of arc constraints in the communication constraint graph. Similarly, the communication features offered by each of the components available in the IP communication library are captured as a set of feature resources together with its cost figures. Then, every communication architecture that can be built using the available components while satisfying all constraints is implicitly considered (as an implementation graph matching the constraint graph) to derive the optimum design solution with respect to the desired cost figure. The corresponding constrained optimization problem is efficiently solved by a novel algorithm that is presented here together with its rigorous theoretical foundations.