Emergency evacuation is the process of movement of people away from the threat or actual occurrence of hazards such as natural disasters, terrorist attacks, fires and bombs. In this paper, we focus on evacuation from a building, but the ideas can be applied to city and region evacuation. We define the problem and show how it can be modeled using graphs. The resulting optimization problem can be formulated as an integer linear program. Though this can be solved exactly, this approach does not scale well for graphs with thousands of nodes and several hundred thousands of edges. This is impractical for large graphs. We study a special case of this problem, where there is only a single source and a single sink. For this case, we give an improved algorithm \emph{Single Source Single Sink Evacuation Route Planner (SSEP)}, whose evacuation time is always at most that of a famous algorithm \emph{Capacity Constrained Route Planner (CCRP)}, and whose running time is strictly less than that of CCRP. We prove this mathematically and give supporting results by extensive experiments. We also study randomized behavior model of people and give some interesting results.