Open list

In the context of search algorithms, particularly those used in artificial intelligence and pathfinding (such as A* search), an open list is a data structure used to store nodes that have been generated but not yet expanded. These nodes represent potential paths or states that the algorithm might explore.

The open list essentially holds candidate nodes that are "waiting" to be evaluated. When an algorithm is searching for a solution, it starts from an initial state (a node). It then generates successor states (neighboring nodes) and adds them to the open list. The algorithm then iteratively selects the "best" node from the open list (according to some heuristic or cost function), expands it (generating its successors), and adds those successors to the open list.

A key characteristic of the open list is that it needs to allow efficient retrieval of the "best" node and efficient insertion of new nodes. Common data structures used for implementing the open list include priority queues (often implemented using heaps), which provide logarithmic time complexity for insertion and retrieval of the minimum (or maximum) element.

The behavior of the open list significantly impacts the performance and characteristics of the search algorithm. For example, A* search uses a heuristic function to estimate the cost to reach the goal from each node in the open list. By choosing the node with the lowest estimated total cost, A* aims to find the optimal path efficiently. Different strategies for managing the open list can lead to different search behaviors, such as breadth-first search (if the open list is a queue) or depth-first search (if the open list is a stack).

Contrastingly, a closed list is used to store nodes that have already been expanded.