—Rate allocation is a fundamental problem in the operation of a wireless network because of the necessity to schedule the operation of mutually interfering links between the nodes. Among the many reasons behind the importance of efficiently determining the membership of an arbitrary rate vector in the feasibility region, is its high relevance in optimal cross layer design. A key feature in a wireless network is that links without common nodes can also conflict (secondary interference constraints). While the node exclusive model problem has efficient algorithms [7], it has long been known that this is a hard problem with these additional secondary constraints [1]. However, wireless networks are usually deployed in geographic areas that do not span the most general class of all graphs possible. This is the underlying theme of this paper, where we provide algorithms for two restricted instances of wireless network topologies. The first tractable instance considers nodes placed arbit...