The recent MPEG Reconfigurable Media Coding (RMC) standard aims at defining media processing specifications (e.g. video codecs) in a form that abstracts from the implementation platform, but at the same time is an appropriate starting point for implementation on specific targets. To this end, the RMC framework has standardized both an asynchronous dataflow model of computation and an associated specification language. Either are providing the formalism and the theoretical foundation for multimedia specifications. Even though these specifications are abstract and platform-independent the new approach of developing implementations from such initial specifications presents obvious advantages over the approaches based on classical sequential specifications. The advantages appear particularly appealing when targeting the current and emerging homogeneous and heterogeneous manycore or multicore processing platforms. These highly parallel computing machines are gradually replacing single-core processors, particularly when the system design aims at reducing power dissipation or at increasing throughput However, a straightforward mapping of an abstract dataflow specification onto a concurrent and heterogeneous platform does often not produce an efficient result Before an abstract specification can be translated into an efficient implementation in software and hardware, the dataflow networks need to be partitioned and then mapped to individual processing elements. Moreover, system performance requirements need to be accounted for in the design optimization process. This paper discusses the state of the art of the combinatorial problems that need to be faced at this design space exploration step. Some recent developments and experimental results for image and video coding applications are illustrated. Both well-known and novel heuristics for problems such as mapping, scheduling and buffer minimization are investigated in the specific context of exploring the design space of dataflow program implementations. (C) 2013 Elsevier B.V. All rights reserved.