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In this paper, we study the wireline two-unicast-Z communication network overdirected acyclic graphs. The two-unicast-Z network is a two-unicast networkwhere the destination intending to decode the second message has apriori sideinformation of the first message. We make three contributions in this paper:  1. We describe a new linear network coding algorithm for two-unicast-Znetworks over directed acyclic graphs. Our approach includes the idea ofinterference alignment as one of its key ingredients. For graphs of a boundeddegree, our algorithm has linear complexity in terms of the number of vertices,and polynomial complexity in terms of the number of edges.  2. We prove that our algorithm achieves the rate-pair (1, 1) whenever it isfeasible in the network. Our proof serves as an alternative, albeit restrictedto two-unicast-Z networks over directed acyclic graphs, to an earlier result ofWang et al. which studied necessary and sufficient conditions for feasibilityof the rate pair (1, 1) in two-unicast networks.  3. We provide a new proof of the classical max-flow min-cut theorem fordirected acyclic graphs.

Alignment based Network Coding for Two-Unicast-Z Networks