Path Optimization and Trusted Routing in MANET: An Interplay Between Ordered Semirings

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 that unambiguously capture the difference between trust and reputation relations. We show that the trustworthiness metrics 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. We consider bottleneck trust and present polynomial time algorithms to obtain the optimal routing paths in various bi-objective settings. In developing these algorithms, we identify an interesting decomposition principle for (min,+) and (min,max) semirings, which yields a distributed solution. Keywords-Pareto Optimality, Lexicographic Optimality, Max-Order Optimality, Semirings.