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For general connections, the problem of finding network codes and optimizingresources for those codes is intrinsically difficult and little is known aboutits complexity. Most of the existing solutions rely on very restricted classesof network codes in terms of the number of flows allowed to be coded together,and are not entirely distributed. In this paper, we consider a new method forconstructing linear network codes for general connections of continuous flowsto minimize the total cost of edge use based on mixing. We first formulate theminimumcost network coding design problem. To solve the optimization problem,we propose two equivalent alternative formulations with discrete mixing andcontinuous mixing, respectively, and develop distributed algorithms to solvethem. Our approach allows fairly general coding across flows and guarantees nogreater cost than any solution without network coding.

Optimization-Based Linear Network Coding for General Connections of Continuous Flows