In this paper, we formulate the problem of trusted routing as a transaction of services over a complex networked environment. We present definitions from service-oriented environments which unambiguously capture the difference between trust and reputation relations. We show that the trustworthiness measures associated with these relations have a linear order embedded in them. Identifying this order structure permits us to treat the trusted routing problem as a bi-objective path optimization problem. Further, we present polynomial time solutions to obtain the optimal routing paths in various biobjective settings. In developing these algorithms, we identify an interesting semiring decomposition principle that yields a distributed solution