In wireless networks, efficient topology improves the performance of network protocols. The previous research mainly focuses on how to construct a cost-efficient network structure from a static and connected topology. Due to lack of continuous connectivity in the underlying topology, most traditional topology control methods are not applicable to the delay or disruption tolerant networks (DTNs). In this paper, we consider the topology control problem in a predictable DTN where the dynamic topology is known a priori or can be predicted over time. First, this dynamic topology is modeled by a directed space-time graph that includes spatial and temporal information. Second, the topology control problem of the predictable DTN is formulated as building a sparse structure. For any pair devices, there is an efficient path connecting them to improve the efficiency of the generated structure. Then, a topology control strategy is proposed for this optimization problem by using a kth shortest paths algorithm. Finally, simulations are conducted on random networks and a real-world DTN tracing date. The results demonstrate that the proposed method can significantly improve the efficiency of the generated structure and reduce the total cost.