Space Information Flow

Network information flow emerged as a fertile research ground over a decade ago, with the advent of network coding that encourages information flows to be encoded when they meet within a data network. In this work, we propose the problem of space information flow — the transmission of information flows in a geometric space, instead of in a fixed, existing network topology. In this new model, information flows are free to propagate along any trajectories in a space, and may be encoded wherever they meet. The goal is to minimize a natural ‘network volume’ that represents the cost of constructing a network, which can support end-to-end unicast and multicast communication demands among terminals at known coordinates. Space information flow models the fundamental problem of information network design, which deserves renewed research attention for taking into account the unique encodability of information flows. We show that designing an information network is indeed different from designing a transportation network. In particular, an optimal multicast network does not necessarily correspond to a Steiner tree, as assumed in past literature. We prove both lower and upper bounds on the cost advantage of network coding (ratio of minimum network cost without coding over that with coding) in geometric multicast network design, and relate the potential benefit of network coding to the Steiner ratio, the cost ratio between a minimum Steiner tree and a minimum spanning tree in geometric spaces.