Floyd Warshall Algorithm
The Floyd Warshall algorithm is a dynamic programming approach to find the shortest paths between all pairs of vertices in a weighted graph. It works well for dense graphs and is capable of handling graphs with both positive and negative weights.
Algorithm Steps:
- Initialize a matrix with direct edge weights.
- Update the matrix with shorter paths found through intermediate vertices:
- For each pair of vertices (i, j), if distance[i][k] + distance[k][j] < distance[i][j], update distance[i][j].
Applications:
- All-pairs shortest path in a weighted graph.
- Routing algorithms in computer networks.
Graph-Based Algorithms for GATE Exam [2024]
Ever wondered how computers figure out the best path in a maze or create efficient networks like a pro? That’s where Graph-Based Algorithms come into play! Think of them as your digital navigation toolkit. As you prepare for GATE 2024, let these algorithms be your allies, unraveling the intricacies of graphs and leading you to success.
Table of Content
- Depth First Search or DFS for a Graph
- Detect Cycle in a Directed Graph
- Topological Sorting
- Bellman–Ford Algorithm
- Floyd Warshall Algorithm
- Shortest path with exactly k edges in a directed and weighted graph
- Biconnected graph
- Articulation Points (or Cut Vertices) in a Graph
- Check if a graph is strongly connected (Kosaraju’s Theorem)
- Bridges in a graph
- Transitive closure of a graph
- Previously Asked GATE Questions on Graph-Based Algorithms
A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(E, V).
In this comprehensive guide, we will explore key graph algorithms, providing detailed algorithm steps with its applications, which are relevance for the GATE Exam.