Bounds and exact values in network encoding complexity with two sinks

For an acyclic directed network with multiple pairs of sources and sinks and a set of Menger's paths connecting each pair of source and sink, it is well known that the number of mergings among these Menger's paths is closely related to network encoding complexity. In this paper, we focus on networks with two distinct sinks and we derive bounds on and exact values of two functions relevant to encoding complexity for such networks.