Resource allocations in stream data processing systems are performed to allocate the resources in a cost-effective manner by formulating the resource allocation problem as a linear program. For a problem with a single output, a backward algorithm or method is used that produces an optimal solution in linear time. For a problem with multiple outputs and the network has a tree structure, a backward shrink algorithm or method is used to provide an optimal solution in linear time. These algorithms are fully distributed, they require only local exchange of parameters between neighboring nodes, and are adaptive to the dynamic changes in network conditions and flow rate fluctuations.