It is widely realized that the integration of database and information retrieval techniques will provide users with a wide range of high quality services. In this paper, we study processing an l-keyword query, p1, p2, …, pl, against a relational database which can be modeled as a weighted graph, G(V, E). Here V is a set of nodes (tuples) and E is a set of edges representing foreign key references between tuples. Let Vi ⊆ V be a set of nodes that contain the keyword pi. We study finding top-k minimum cost connected trees that contain at least one node in every subset Vi, and denote our problem as GST-k. When k = 1, it is known as a minimum cost group Steiner tree problem which is NP-Complete. We observe that the number of keywords, l, is small, and propose a novel parameterized solution, with l as a parameter, to find the optimal GST-1, in time complexity O(3l n + 2l ((l + log n)n + m)), where n and m are the numbers of nodes and edges in graph G. Our solution can handle graphs with a large number of nodes. Our GST-1 solution can be easily extended to support GST-k, which outperforms the existing GST-k solutions over both weighted undirected/directed graphs. We conducted extensive experimental studies, and report our finding.