Time-Aggregated Graphs for Modeling Spatio-temporal Networks

Given applications such as location based services and the spatio-temporal queries they may pose on a spatial network (e.g., road networks), the goal is to develop a simple and expressive model that honors the time dependence of the road network. The model must support the design of efficient algorithms for computing the frequent queries on the network. This problem is challenging due to potentially conflicting requirements of model simplicity and support for efficient algorithms. Time expanded networks, which have been used to model dynamic networks employ replication of the networks across time instants, resulting in high storage overhead and algorithms that are computationally expensive. In contrast, the proposed time-aggregated graphs do not replicate nodes and edges across time; rather they allow the properties of edges and nodes to be modeled as a time series. Since the model does not replicate the entire graph for every instant of time, it uses less memory and the algorithms for common operations are computationally more efficient than for time expanded networks. One important query on spatio-temporal networks is the computation of shortest paths. Shortest paths can be computed either for a given start time or to find the start time and the path that lead to least travel time journeys (best start time journeys). Developing efficient algorithms for computing shortest paths in a time variant spatial network is challenging because these journeys do not always display optimal prefix property, making techniques like dynamic programming inapplicable. In this paper, we propose algorithms for shortest path computation for a fixed start time. We present the analytical cost model for the algorithm and compare with the performance of existing algorithms.