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The trustworthiness of service providers plays an important role when a consumer selects a service. This paper studies the problem of how to efficiently search and select trustworthy service providers for users in social networks consisting of service providers and consumers. A trust value between two participants can be derived by existing methods from the optimal trust path between them in a social network. When more than one trust factors are taken into consideration, the exact optimal trust path selection algorithm is NP-complete. Although several heuristic algorithms have been proposed to find approximate solutions, their time complexities are still too high to be acceptable in practice, especially when they are used in very large scale social networks. Focusing on reducing trust path searching time, this paper proposes an efficient preprocessing-based search strategy. It exploits structural properties of the social networks and builds an advanced data structure from preprocessing, which can be used to simplify and accelerate the trust path searching. Experimental results show our strategy is very efficient and nearly achieves a constant time complexity. The computed trustworthiness based on our method has excellent performance close to that of the best existing heuristic algorithm.