Admissibility of A* Search
Under certain conditions, A* search will always reach a goal state and be able to identify a shortest path to that state as soon as it arrives there.
h’(s) must not exceed h(s) for any s.
w(si, sj) > 0 for all si and sj.
This property of being able to find a shortest path to a goal state is known as the admissibility property of A* search.
Sometimes we say that a particular A* algorithm is admissible. We can say this when its h’ function satisfies the underestimation condition and the underlying search problem involves positive weights.