The widespread deployment of web services and the rapid development of big data applications bring in new challenges to web service compositions in the context of big data. The large number of web services processing a huge amount of diverse data together with the complex and dynamic relationships among the services require automatic composition of semantic web services to perform quickly, thereby demanding fast and cost-effective service composition algorithms. In this paper, we investigate the web service composition in big data environments by proposing novel composition algorithms with low time-complexity. In our proposed algorithm, we decompose the service composition into three stages: construction of parameter expansion graphs, transformation of service dependence graphs, and backtracking search for service compositions. Based on the parameter expansion strategies, we then propose two fast service composition algorithms, for which we also analyse their time complexities. We conduct comparison experimentally to evaluate the performance of the algorithms and validate their effectiveness using a big semantic service dataset. Our results reveal that the proposed approaches are more preferable than a well-known algorithm in terms of execution time and precision.