Concepts8

Bidirectional BFS searches forward from the start and backward from the goal to meet in the middle, drastically reducing explored states.

SPFA is a queue-based optimization of Bellman–Ford that only relaxes edges from vertices whose distance just improved.

Dijkstra's algorithm finds shortest path distances from one source to all vertices when all edge weights are non-negative.

Bellman–Ford finds single-source shortest paths even when some edge weights are negative.

Dijkstra’s algorithm can be adapted to track the second shortest path by keeping the best and second-best distances per vertex.

Breadth-First Search (BFS) explores a graph level by level, visiting all vertices at distance d from the source before any at distance d+1.

Multi-source BFS explores an unweighted graph starting from several sources at once to compute the minimum distance to any source for every vertex.

0-1 BFS is a shortest path algorithm specialized for graphs whose edge weights are only 0 or 1.