  We investigate the two unicast flow problem over layered linear deterministic
networks with arbitrary number of nodes. When the minimum cut value between
each source-destination pair is constrained to be 1, it is obvious that the
triangular rate region {(R_1,R_2):R_1,R_2> 0, R_1+R_2< 1} can be achieved, and
that one cannot achieve beyond the square rate region {(R_1,R_2):R_1,R_2> 0,
R_1< 1,R_2< 1}. Analogous to the work by Wang and Shroff for wired networks, we
provide the necessary and sufficient conditions for the capacity region to be
the triangular region and the necessary and sufficient conditions for it to be
the square region. Moreover, we completely characterize the capacity region and
conclude that there are exactly three more possible capacity regions of this
class of networks, in contrast to the result in wired networks where only the
triangular and square rate regions are possible. Our achievability scheme is
based on linear coding over an extension field with at most four nodes
performing special linear coding operations, namely interference neutralization
and zero forcing, while all other nodes perform random linear coding.
