Uniform-cost search

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Graph search algorithms
Search A* B* Bellman-Ford algorithm Best-first search Bidirectional search Breadth-first search Depth-first search Depth-limited search Dijkstra's algorithm Floyd-Warshall algorithm Hill climbing Iterative deepening depth-first search Johnson's algorithm Uniform-cost search

In computer science, uniform-cost search (UCS) is a tree search algorithm used for traversing or searching a weighted tree, tree structure, or graph. Intuitively, the search begins at the root node. The search continues by visiting the next node which has the least total cost from the root. Nodes are visited in this manner until a goal state is reached.

Typically, the search algorithm involves expanding nodes by adding all unexpanded neighboring nodes that are connected by directed paths to a priority queue. In the queue, each node is associated with its total path cost from the root, where the least-cost paths are given highest priority. The node at the head of the queue is subsequently expanded, adding the next set of connected nodes with the total path cost from the root to the respective node. The uniform-cost search is complete and optimal if the cost of each step exceeds some positive bound ε.^[1]

Dijkstra's algorithm, which is perhaps better-known, can be regarded as a variant of uniform-cost search, where there is no goal state and processing continues until all nodes have been removed from the priority queue. As in Dijkstra's algorithm, UCS guarantees that (if all edge weights are non-negative) the shortest path to a particular node has been found once the node is extracted from the priority queue.

Uniform-cost search is a special case of the A* search algorithm if its heuristic is a constant function. Breadth-first search (BFS) is a special case of uniform-cost search when all edge costs are positive and identical. Where BFS first visits the node with the shortest path length (number of nodes) from the root node, UCS first visits the node with the shortest path costs (sum of edge weights) from the root node.