Articulation Points (or Cut Vertices) in a Graph
Articulation points are vertices whose removal would disconnect a graph. Detecting these points is essential in network design to ensure robustness and fault tolerance. Algorithms for finding articulation points often use depth-first search.
Algorithm Steps:
- Use DFS to traverse the graph, maintaining information about discovery time and low value for each vertex.
- For each edge (u, v), if v is not visited, recursively call DFS for v.
- Update the low value of u based on the low value of v.
- If the low value of v is greater than or equal to the discovery time of u, u is an articulation point.
Applications:
- Network design for robustness.
- Fault detection in systems.
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.