The Knight’s Tour: A Classic Chessboard Challenge
The Knight’s Tour is a fascinating problem from the domain of computer science and mathematics, specifically within the realm of graph theory. The problem presents a curious challenge: Can a knight traverse every square of a chessboard exactly once? The Knight’s Tour Statement On a given N x N chessboard, determine if a knight can...
Travelling Salesman Problem: Seeking the Shortest Route
The Travelling Salesman Problem (TSP) is a classic optimization problem in the realm of computer science and operations research. The problem can be stated simply: Given a set of cities and the distances between them, what’s the shortest possible route that allows a salesman to visit each city once and then return to the starting...
Kosaraju’s Algorithm: Strongly Connected Components
Introduction In the world of graph theory, one concept that stands out in terms of its practical relevance and intriguing nature is that of Strongly Connected Components (SCCs). An SCC in a directed graph is a maximal subgraph in which every pair of vertices (u, v) and (v, u) is reachable from each other. Kosaraju’s...
Hamiltonian Cycle: Traversing Every Vertex Once
The world of graph theory is vast and intriguing, filled with puzzles and problems that have both stumped and inspired mathematicians and computer scientists for centuries. Among these is the Hamiltonian Cycle problem, a popular topic that brings together complexity, utility, and the challenge of visiting every vertex in a graph exactly once. What...
Eulerian Path and Eulerian Circuit: Fleury’s Algorithm
The world of graph theory is vast and intriguing, and among its many fascinating concepts, the Eulerian Path and Eulerian Circuit stand out. These are paths and circuits in a graph that visit every edge exactly once. This article delves deep into the concept of Eulerian paths and circuits, particularly emphasizing the Fleury’s algorithm and...
Bridges in Graphs: DFS-Based Algorithm Explored
Graph theory, a domain of mathematics that studies the intricate relationships and properties of graphs, holds a multitude of algorithms for various problems. Among the fascinating topics is the study of ‘bridges’ in a graph. Understanding Bridges In graph theory, a bridge (or cut-edge) is an edge whose removal would increase the...
Articulation Points – Tarjan’s Algorithm (DFS based)
Articulation points, also known as cut vertices, play a significant role in understanding the vulnerability and fault tolerance of networks. In graph theory, an articulation point is a vertex that, when removed along with associated edges, makes the graph disconnected. For a connected graph, it means its removal increases the number of connected...
Topological Sorting: Using Depth-First Search (DFS)
Topological Sorting is a linear ordering of vertices in a directed acyclic graph (DAG) so that for every directed edge uv, vertex u comes before v in the ordering. This method is particularly useful in scheduling tasks with dependencies, as it provides a way to order tasks so that each task only begins after its...
Prim’s Algorithm: A Deep Dive into Minimum Spanning Trees
Graphs, intricate structures representing a network of nodes and edges, have a wide range of applications. When it comes to connecting all these nodes with the least possible weight, Minimum Spanning Trees (MSTs) come into play. Among the various algorithms designed to find MSTs, Prim’s algorithm stands out for its simplicity and efficiency....
Breadth-First Search (BFS) in Graphs with JavaScript
Breadth-First Search (BFS) is a versatile graph traversal algorithm with a wide range of applications. Used to traverse through nodes of a graph in a breadthward motion, BFS employs a layer-by-layer approach, visiting all the nodes of a depth before proceeding to the next level. Understanding Breadth-First Search The BFS algorithm starts its...