A Delaunay Triangulation Approach to Space Information Flow

In contrast to network information flow proposed by Ahlswede et al., Space Information Flow (SIF) studies network coding in a geometric space such as a Euclidean space, in which additional relay nodes are allowed for reducing the communication cost. This work focuses on the problem of mincost multicast network coding in 2-D Euclidean space. We prove several properties of an optimal solution to the problem, and propose a new polynomial-time heuristic algorithm, combining techniques of Delaunay triangulation and non-uniform partitioning. The introduction of Delaunay triangulation aims to adapt the new algorithm to any density distribution of relay and terminal nodes, while non-uniform partitioning can handle any density distribution among terminal nodes. The two complementary techniques work in concert to eliminate an approaching-infinity problem that recent algorithms are known to be prone of, and consequently make the new algorithm fast-converging. Theoretic analysis and simulation results verify the effectiveness of the new algorithm.