Computing 2-terminal reliability for radio-broadcast networks

The authors present a probabilistic graph model for radio broadcast networks where nodes fail randomly and the edges are perfectly reliable. This model can represent the general case where both the nodes and edges can fail. Using this model, it is shown that the two-terminal reliability problem for radio broadcast networks is computationally difficult, in particular #P-complete, even in two important restricted cases. Efficient bounding techniques based on subgraph counts and vertex-packing methods are presented. The subgraph counting and vertex-packing bounds are the counterparts of the subgraph counting and edge-packing bounds for wired point-to-point networks with reliable nodes and unreliable links. The authors define series and parallel node reductions for arbitrary networks with unreliable nodes and reliable edges, and they incorporate these reductions into a new polynomial-time algorithm to improve the vertex-packing bounds via approximation by series-parallel reducible graphs