Minimum Spanning Tree (MST)
A minimum spanning tree (MST) of a connected undirected graph is a subgraph that includes the all the vertices of graph with the minimum possible total edge weight. The MSTs have the various applications in the network design, circuit wiring and clustering algorithms.
Algorithm Steps:
- Start with the any vertex as the initial tree.
- At each step, add the minimum weight edge that connects a vertex in the tree to the vertex outside the tree.
- Repeat the process until all vertices are included in tree.
Applications:
- Network design to minimize infrastructure costs.
- Circuit design to the minimize wire usage.
- Cluster analysis in the data mining and machine learning.
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.