The widespread deployment of web services and 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 be performed quickly, thereby demanding more efficient service composition algorithms. In this paper, we investigate the issue of web service composition in big data environments by proposing novel composition algorithms with low time-complexity. Specifically, 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 efficient semantic web service composition algorithms and analyze their time complexity. We also conduct comparison experimentally to evaluate the efficiency of the algorithms and validate their effectiveness using a big data (service composition) set.