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In this paper, the authors study the problem of utility maximization in P2P systems, in which aggregate application specific utilities are maximized by running distributed algorithms on P2P nodes, which are constrained by their uplink capacities. For certain P2P topologies, they show that routing along a linear number of trees per source can achieve the largest rate region that can be possibly obtained by intra-session and inter-session network coding. This observation allows one to develop a simple multi-tree formulation for the problem. For the resulting non-strictly concave optimization problem, they develop a primal-dual distributed algorithm and prove its global convergence using their proposed sufficient conditions.
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