Topological Sorting
Topological sorting is vital for scheduling tasks with dependencies, and it is often used in project management and task scheduling. The algorithm involves linearly ordering the vertices of a directed acyclic graph (DAG) in such a way that for every directed edge ‘uv,’ vertex ‘u’ comes before ‘v’ in the ordering.
Algorithm Steps:
- Start DFS from any unvisited vertex.
- Mark the current vertex as visited.
- Recursively call DFS for each adjacent vertex.
- Add the current vertex to the topological order after recursion.
- The final order is the reverse of the order in which vertices are added.
Applications:
- Task scheduling with dependencies.
- Build systems to determine order of compilation.
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.