Space Information Flow: Multiple Unicast

The multiple unicast network coding conjecture states that for multiple unicast in an undirected network, network coding is equivalent to routing. Simple and intuitive as it is, the conjecture has remained open since its proposal in 2004,, and is now a well-known unsolved problem in the field of network coding. In this paper, the authors provide a proof to the conjecture in its space/geometric version. Space information flow is a new paradigm being proposed. It studies the transmission of information in a geometric space, where information flows are free to propagate along any trajectories, and may be encoded wherever they meet.