Modern experimental technology enables the identification of the sensory proteins that interact with the cellsí environment or various pathogens. Expression and knockdown studies can determine the downstream effects of these interactions. However, when attempting to reconstruct the signaling networks and pathways between these sources and targets, one faces a substantial challenge. Although pathways are directed, high-throughput protein interaction data is undirected. In order to utilize the available data, we need methods that can orient protein interaction edges and discover high-confidence pathways that explain the observed experimental outcomes. We formalized the orientation problem in weighted protein interaction graphs as an optimization problem and present three approximation algorithms based on either weighted Boolean satisfiability solvers or probabilistic assignments. We used these algorithms to identify pathways in yeast. Our approach recovers twice as many known signaling cascades as a recent unoriented signaling pathway prediction technique and over thirteen times as many as an existing network orientation algorithm. The discovered paths match several known signaling pathways and suggest new mechanisms that are not currently present in signaling databases. For some pathways, including the pheromone signaling pathway and the high osmolarity glycerol pathway, the method suggests interesting and novel components that extend current annotations.