Shortest Path Algorithms for a Fixed Start Time
Shortest path computation is an important query on any network. In a spatio-temporal network, this computation assumes added semantics due to the dependence of network attributes on time. Shortest paths can be computed either for a given start time or to find the start time and the path that leads to least travel time journeys (best start time journeys). Developing efficient algorithms for computing shortest paths in a time varying spatial network is challenging because these journeys do not always display greedy property or optimal substructure. This chapter describes algorithms to compute shortest paths for a given start time. The formulations of shortest path algorithms can also depend on the properties of the network parameters such as travel times. For example, the algorithm can significantly vary depending on whether the travel times follow FIFO property or not. The chapter provides algorithms for both FIFO and non-FIFO travel times.