Finding the Cost-Optimal Path with Time Constraint over Time-Dependent Graphs

Shortest path query is an important problem and has been well studied in static graphs. However, in practice, the costs of edges in graphs always change over time. We call such graphs as timedependent graphs. In this paper, we study how to find a costoptimal path with time constraint in time-dependent graphs. Most existing works regarding the Time-Dependent Shortest Path (TDSP) problem focus on finding a shortest path with the minimum travel time. All these works are based on the following fact: the earliest arrival time at a vertex v can be derived from the earliest arrival time at v’s neighbors. Unfortunately, this fact does not hold for our problem. In this paper, we propose a novel algorithm to compute a cost-optimal path with time constraint in time-dependent graphs. We show that the time and space complexities of our algorithm are O(kn log n + mk) and O((n + m)k) respectively. We confirm the effectiveness and efficiency of our algorithm through conducting experiments on real datasets with synthetic cost.