I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance from the source.

In *best-first* search algorithms, the node to expand next is the most promising one according to some evaluation function (which may take into account the current global knowledge). In the normal A* algorithm, the evaluation function is the sum of the length of the currently know shortest path from the source and the heuristic estimate of the distance to the goal. Is there a standard term for a similar strategy where the evaluation function is just the heuristic distance to the goal?

I was thinking about *greedy* and *hill-climbing*, but *greedy* in this context seems to be just a synonym of *best-first*, and in what is commonly referred to as *hill-climbing*, there seems to be either no backtracking, or just one-step backtracking, that is, old unexpanded nodes are discarded at each step.