Computing 2-Terminal Reliability for Radio-Broadcast Networks

Reader Aids — Purpose: Present a new method Special math needed for explanations: Graph theory Specal math needed to use results: Same Results useful to: Network designers & Conclusions — The 2-terminal reliability of a network is the probability that there exists an operating path from a source node to a sink node. Computing this measure is a difficult problem that has been studied extensively for wired point-to-point networks. However, little is known about the problem for radio broadcast networks. In this paper we 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 nodes and edges can fail. Using this model, we show that the 2-terminal reliability problem for radio broadcast networks is computationally difficult, in particular, #P-complete, even in two important restricted cases. We present efficient bounding techniques based on subgraph counts and vertex-packing methods. The subgraph counting and vertex-packing bounds are the counterpart of the subgraph counting and edge-packing bounds for wired point-to-point networks with reliable nodes and unreliable links. Further, we define series and parallel node reductions for arbitrary networks with unreliable nodes and reliable edges, and incorporate these reductions into a new polynomial time algorithm to improve the vertex-packing bounds via approximation by series-parallel reducible graphs.