The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the time-dependent shortest-path problem. A time-dependent graph GT is a graph that has an edge-delay function, wi,j(t), associated with each edge (vi, vj), to be stored in a database. The edge-delay function wi,j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A user-specified query is to ask the minimum-travel-time path, from a source node, vs, to a destination node, ve, over the time-dependent graph, GT , with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT . The challenge of this problem is the a...