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In a multi-hop wireless network, wireless interference is crucial to the Maximum Multi-Flow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks. In this paper, the authors observe that network coding could help to decrease the impacts of wireless interference, and propose a framework to study the MMF problem for multi-hop wireless networks with network coding. Firstly, a network model is set up to describe the new conflict relations modified by network coding. Then, they formulate a linear programming problem to compute the maximum throughput and show its superiority over one in networks without coding. Finally, the MMF problem in wireless network coding is shown to be NP-hard and a polynomial approximation algorithm is proposed.
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