Range Assignment for Biconnectivity and k-Edge Connectivity in Wireless Ad Hoc Networks

Depending on whether bidirectional links or unidirectional links are used for communications, the network topology under a given range assignment is either an undirected graph referred to as the bidirectional topology, or a directed graph referred to as the unidirectional topology. The Min-Power Bidirectional (resp., Unidirectional) k-Node Connectivity problem seeks a range assignment of minimum total power subject to the constraint that the produced bidirectional (resp. unidirectional) topology is k-vertex connected. Similarly, the Min-Power Bidirectional (resp., Unidirectional) k-Edge Connectivity problem seeks a range assignment of minimum total power subject to the constraint the produced bidirectional (resp., unidirectional) topology is k-edge connected.