Analysis of the trust network proves beneficial to the users in Online Social Networks (OSNs) for decision-making. Since the construction of trust propagation paths connecting unfamiliar users is the preceding work of trust inference, it is vital to find appropriate trust propagation paths. Most of existing trust network discovery algorithms apply the classical exhausted searching approaches with low efficiency and/or just take into account the factors relating to trust without regard to the role of distrust relationships. To solve the issues, we first analyze the trust discounting operators with structure balance theory and validate the distribution characteristics of balanced transitive triads. Then, Maximum Indirect Referral Belief Search (MIRBS) and Minimum Indirect Functional Uncertainty Search (MIFUS) strategies are proposed and followed by the Optimal Trust Inference Path Search (OTIPS) algorithms accordingly on the basis of the bidirectional versions of Dijkstra's algorithm. The comparative experiments of path search, trust inference and edge sign prediction are performed on the Epinions data set. The experimental results show that the proposed algorithm can find the trust inference path with better efficiency and the found paths have better applicability to trust inference.