Topology design for time-varying networks

Traditional wireless networks seek to support end-to-end communication through either a single-hop wireless link to infrastructure or multi-hop wireless path to some destination. However, in some wireless networks (such as delay tolerant networks, or mobile social networks), due to sparse node distribution, node mobility, and time-varying network topology, end-to-end paths between the source and destination are not always available. In such networks, the lack of continuous connectivity, network partitioning, and long delays make design of network protocols very challenging. Previous DTN or time-varying network research mainly focuses on routing and information propagation. However, with large number of wireless devices’ participation, and a lot of network functionality depends on the topology, how to maintain efficient and dynamic topology of a time-varying network becomes crucial. In this dissertation, I model a time-evolving network as a directed time-space graph which includes both spacial and temporal information of the network, then I study various topology control problems with such time-space graphs. First, I study the basic topology design problem where the links of the network are reliable. It aims to build a sparse structure from the original time-space graph such that (1) the network is still connected over time and/or supports efficient routing between any two nodes; (2) the total cost of the structure is minimized. I first prove that this problem is NP-hard, and then propose several greedy-based methods as solutions. Second, I further study a cost-efficient topology design problem, which not only requires the above two objective, but also guarantees that the spanning ratio of the topology is bounded by a given threshold. This problem is also NP-hard, and I give several greedy algorithms to solve it. Last, I consider a new topology design problem by relaxing the assumption of reliable links. Notice that in wireless networks the topologies are not quit predictable and the links are often unreliable. In this new model, each link has a probability to reflect its reliability. The new reliable topology design problem aims to build a sparse structure from the original space-time graph such that (1) for any pair of devices, there is a space-time path connecting them with the reliability larger than a required threshold; (2) the total cost of the structure is minimized. Several heuristics are proposed, which can significantly reduce the total cost of the topology while maintain the connectivity or reliability over time. Extensive simulations on both random networks and real-life tracing data have been conducted, and results demonstrate the efficiency of the proposed methods