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In delay tolerant networks (DTNs), the lack of continuous connectivity, network partitioning, and long delays make design of network protocols very challenging. Previous DTN research mainly focuses on routing and information propagation. However, with a large number of wireless devices' participation, it becomes crucial regarding how to maintain efficient and dynamic topology of the DTN. In this paper, we study the topology control problem in a predictable DTN, where the time-evolving network topology is known a priori or can be predicted. We first model such time-evolving network as a directed space-time graph that includes both spacial and temporal information. The aim of topology control is to build a sparse structure from the original space-time graph such that 1) the network is still connected over time and supports DTN routing between any two nodes; 2) the total cost of the structure is minimized. We prove that this problem is NP-hard, and propose two greedy-based methods that can significantly reduce the total cost of topology while maintaining the connectivity over time. We also introduce another version of the topology control problem by requiring that the least cost path for any two nodes in this constructed structure is still cost-efficient compared with the one in the original graph. Two greedy-based methods are provided for such a problem. Simulations have been conducted on both random DTN networks and real-world DTN tracing data. Results demonstrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]