What are the common algorithms for searching within graphs?

Common algorithms for searching within graphs include Depth-First Search (DFS), Breadth-First Search (BFS), Dijkstra's Algorithm, and A* Search.

Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It uses a stack data structure to remember to get back to the start point when no further way is found. DFS is often used in topological sorting, scheduling problems, cycle detection in graphs, and pathfinding in maze puzzles.

Breadth-First Search (BFS) is another graph traversal algorithm that explores all the vertices of a graph in breadth-first order, i.e., it explores all the vertices at the current depth before moving on to vertices at the next depth level. BFS uses a queue data structure to keep track of the vertices to visit next. It is often used in shortest path problems, serialization/deserialization of a binary tree, and in cycle detection in undirected graph.

Dijkstra's Algorithm is a graph search algorithm that solves the shortest-path problem for a graph with non-negative edge path costs, producing a shortest path tree. This algorithm uses a priority queue data structure and is used in network routing protocols, such as OSPF and IS-IS.

A* Search is a graph traversal and path search algorithm, which is often used in many fields of computer science due to its completeness, optimality, and optimal efficiency. It uses a best-first search and finds the least-cost path from a given initial node to one goal node. It is widely used in pathfinding and graph traversal, the process of plotting an efficiently traversable path between multiple points, such as GPS navigation and games.

Each of these algorithms has its own strengths and weaknesses, and the choice of which to use depends on the specific requirements of the problem at hand. For example, if you need to find the shortest path between two nodes, Dijkstra's Algorithm or A* Search would be appropriate. If you simply need to traverse the entire graph, DFS or BFS might be more suitable.