Page "A* search algorithm" Paragraph 10

Starting with the initial node, it maintains a priority queue of nodes to be traversed, known as the open set.

The lower for a given node, the higher its priority.

At each step of the algorithm, the node with the lowest value is removed from the queue, the and values of its neighbors are updated accordingly, and these neighbors are added to the queue.

The algorithm continues until a goal node has a lower value than any node in the queue ( or until the queue is empty ).

( Goal nodes may be passed over multiple times if there remain other nodes with lower values, as they may lead to a shorter path to a goal.

) The value of the goal is then the length of the shortest path, since at the goal is zero in an admissible heuristic.

If the actual shortest path is desired, the algorithm may also update each neighbor with its immediate predecessor in the best path found so far ; this information can then be used to reconstruct the path by working backwards from the goal node.

Additionally, if the heuristic is monotonic ( or consistent, see below ), a closed set of nodes already traversed may be used to make the search more efficient.