Bellman–Ford Algorithm
The Bellman–Ford algorithm is employed for finding the shortest paths from a single source vertex to all other vertices in a weighted graph, even if the graph contains negative weight edges. This algorithm is particularly useful in scenarios where Dijkstra’s algorithm might fail due to negative weights.
Algorithm Steps:
- Initialize distances from the source vertex to all others as infinity.
- Set the distance to the source as 0.
- Relax edges iteratively:
- For each edge (u, v), if distance[u] + weight(u, v) < distance[v], update distance[v].
- Repeat step 3 for V-1 times, where V is the number of vertices.
- Detect negative cycles by checking for further relaxation after V-1 iterations.
Applications:
- Single-source shortest path with negative weight edges.
- Network routing protocols.
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.