Best-first search algorithms have been widely used to find a minimum cost path in graph
search. To formulate certain problems involving temporal events, it is at times instrumental to
use graphs whose edge costs are time-dependent. In such a graph, shortest paths are dependent
on time at which traversal in the graph begins. Typically, structural changes in sst occur at
discrete points in t, where sst is the shortest path with start time t. In this paper, a best-first
algorithm is generalized to handle time-dependent graphs to find shortest paths together with
their start time characteristics and some properties of the algorithm are investigated.