Several high-throughput distributed data-processing applications require multi-hop processing of streams of data. These applications include continual processing on data streams originating from a network of sensors, composing a multimedia stream through embedding several component streams originating from different locations, etc. These data-flow computing applications require multiple processing nodes interconnected according to the data-flow topology of the application, for on-stream processing of the data. Since the applications usually sustain for a long period, it is important to optimally map the component computations and communications on the nodes and links in the network, fulfilling the capacity constraints and optimizing some quality metric such as end-to-end latency. The mapping problem is unfortunately NP-complete and heuristics have been previously proposed to compute the approximate solution in a centralized way. However, because of the dynamicity of the network, it is practically impossible to aggregate the correct state of the whole network in a single node. In this paper, we present a distributed algorithm for optimal mapping of the components of the data flow applications. We propose several heuristics to minimize the message complexity of the algorithm while maintaining the quality of the solution.