Floyd-Warshall Algorithm
The Floyd-Warshall algorithm is a dynamic programming algorithm used to find the shortest paths between all pairs of vertices in a weighted graph. Unlike other algorithms such as Dijkstra’s, which computes the shortest path from a single source to all other vertices, the Floyd-Warshall algorithm computes the shortest paths between every pair of vertices.
Key Concepts:
All-Pairs Shortest Path: The algorithm computes the shortest paths between every pair of vertices in a graph.
Dynamic Programming: The algorithm builds a solution incrementally by considering all possible paths between vertices, step by step.
Negative Weights: The algorithm can handle graphs with negative edge weights but does not work with graphs that have negative weight cycles (cycles where the total weight of the cycle is negative)
Real-World Applications:
Routing in Networks: Floyd-Warshall is used in network routing algorithms to find the shortest paths between all pairs of routers, ensuring efficient data transmission in a computer network.
Example: Internet routers can use Floyd-Warshall to determine the shortest paths for routing packets across different regions of the network.
Flight Scheduling: Airlines can use this algorithm to find the shortest travel times between any pair of airports, taking into account possible layovers.
Example: Finding the minimum travel time between two cities with the option of passing through multiple connecting airports.
Social Networks: The algorithm is used in analyzing social networks to find the shortest chain of connections between any two individuals.
Example: Finding the smallest degree of separation between two users in a social network (like LinkedIn or Facebook).