I am unclear as to why the conditions for optimality for A* search are different for graph search and tree search. When discussing conditions for optimality for A* search in Russell and Norvig's Artificial Intelligence: A Modern Approach they say:The first condition we require for optimality is that $h(n)$ be an admissible heuristic. ...A second, slightly stronger condition called consistency (or sometimes monotonicity) is required only for applications of A* to graph search.Why is consistency only required for A* graph search and not A* tree search? Why are the conditions for optimality different for the two types of search?
Why are the conditions for optimality different for A* tree and graph search?
algorithms;graphs;search algorithms;heuristics