Revisiting the linear information flow algorithm. (1st January 2013) - Higgs, Russell
In this short paper, we reprise a geometrical proof of the deterministic linear information flow algorithm for a multicast network. Each time this greedy algorithm is run, it can always construct a linear network code from the underlying graph, provided the alphabet used contains at least as many elements as the number, n, of receivers in the network. Our proof actually shows that this lower bound can be reduced to the maximum number of receivers any coding point is connected to along the chosen disjoint path sets. The main result we give is to show how greedy the algorithm can be by giving an example of a network graph with n receivers, that needs an alphabet of size n to implement the algorithm for each n ≥ 2, but which in reality only requires a binary alphabet.