## Shortest Path Problem-

• In general, Shortest path problem is a problem of finding the shortest path(s) between vertices or nodes in the given graph.
• Shortest path between two vertices is a path that has the least cost as compared to all other paths that exists in the graph.

## Shortest Path Algorithms-

• Shortest path algorithms are a family of algorithms used for solving shortest path problem.
• Shortest path algorithms have a wide range of applications such as in-

1. Google Maps
2. Road Networks
3. Logistics Research

## Types of Shortest Path Problem-

There are different types of shortest path problem-

1. Single-pair shortest path problem
2. Single-source shortest path problem
3. Single-destination shortest path problem
4. All pairs shortest path problem ### 1. Single-pair shortest path problem-

• Single-pair shortest path problem is a shortest path problem in which we find out the shortest path between a pair of vertices of the given graph.
• A* Search Algorithm is a famous algorithm used for solving single-pair shortest path problem.

### 2. Single-source shortest path problem-

• Single-source shortest path problem is a shortest path problem in which we find out the shortest paths from a given source vertex to all the other remaining vertices of the given graph.
• Dijkstra’s Algorithm and Bellman Ford Algorithm are the famous algorithms used for solving single-source shortest path problem.

### 3. Single-destination shortest path problem-

• Single-destination shortest path problem is a shortest path problem in which we find out the shortest paths from all the vertices to a single destination vertex of the given graph.
• By reversing the direction of each edge in the graph, this problem is reduced to a single-source shortest path problem.
• Dijkstra’s Algorithm is a famous algorithm adapted for solving single-destination shortest path problem.

### 4. All pairs shortest path problem-

• All pairs shortest path problem is a shortest path problem in which we find out the shortest paths between every pair of vertices of the given graph.
• Floyd-Warshall Algorithm and Johnson’s Algorithm are the famous algorithms used for solving All pairs shortest path problem.

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