Recently, graph-based representations have gained enormous popularity for simulating real-world data. Cliques are a key issue in graph theory that is used to solve numerous mathematical issues and create graphs. Cliques are extensively researched in the field of computer science, with the clique problem assessing if a clique having a certain size within a graph is NP-complete.  Yet, in spite of all complexities, there has been research into several techniques for finding cliques. What Are Cliques? In all undirected graphs G = (N, E), a clique, is a "subset of the nodes", so that all pairs of distinct nodes is ... Read More

How Do Graphs Work? A group of things that are connected is referred to as a graph. They may represent anything at all, from based on merely mathematical ideas, to real-life objects, events and occurrences. For instance, a graph represents a list of individuals with a family connection. Similarly, a network of metropolitan areas is linked together by roadways. Typically, we describe the elements of the network as nodes or vertices, while the links among them are referred to as edges or arcs. Pic 1 − Visual Representation of a Graph with Nodes and Edges Unweighted Graph: What Is ... Read More

Even with limitless time, algorithms are unable to resolve all computer problems. The answer to NP-complete problems remains unknown. It's worth noting that when single NP-complete issue is able to be answered in polynomial time, then all others may be resolved as well. Dense Subgraph A dense subgraph is one that has numerous edges for each vertex in the theory of graphs and computer science. Clique A clique constitutes a subsection of a graph in which every vertex is linked to every other vertex, making the "subgraph" a full graph.  "Maximal Clique Problem" aims for locating the largest clique in ... Read More

There is no solution to "NP-complete" problems. So far, there hasn't been a polynomial time method developed for any NP-complete problem, nor has anyone shown that there isn't one. There is an intriguing fact about NP-complete problems: if one manages to be resolved under polynomial time, all are within reach. In this post, we'll prove that a problem comprising an independent set and clique is NP-Complete. Clique A clique refers to a "subgraph" of a graph in which every node is connected to one another, implying that the subsection is a complete graph. NP-Class The NP in the NP class ... Read More

The travelling salesman problem is a popular topic in AI and operational research. Since its first articulation, a plethora of publications have been written providing various solutions to this problem. Furthermore, a slew of novel formulations has been presented by associated practitioners in an attempt to broaden the application of the fundamental TSP. Travelling Salesman Problem: Definition Formally defined, the travelling salesman problem (TSP) is as follows - Discover the shortest way that covers each city "precisely once and returns to the initial city" when provided with a collection of cities and distances between each city. More On The Problem ... Read More

Even with infinite time, there are some computing issues that algorithms cannot resolve. NP-complete problems are those whose solution is unknown. It's intriguing to note that if one NP-complete question can be resolved in polynomial time, subsequently, all others can be resolved. In this study, we will define a sparse graph, discuss several complexity classes, independent sets, and demonstrate that sparse graphs are NP-complete. What Is A Sparse Graph? A sparse graph is one with a limited number of edges. The total number of edges in this situation is significantly fewer than there could be or the highest possible number ... Read More

Graph coloring is a subset of graph labelling in graph theory. The use of colors stems from coloring the nations on a map, wherein each face is colored. There are several real-world applications for graph coloring, as well as issues of theory. Apart from the traditional forms of problems, other constraints can be imposed on the graph, the manner a color is given, or even the color itself. It has even gained widespread appeal in the shape of the renowned numerical puzzle Sudoku. Graph coloring remains an active area of study. What Is Vertex Coloring? The assignment of colors or ... Read More

Pathfinding algorithms are based on graph search techniques that study paths between nodes, starting with one node and progressing via connections until the objective is attained. In this post, we'll talk about weighted graphs and how to calculate the monotonic shortest route between source and end node in a directed weighted graph. What Are Weighted Graphs? A weighted graph combines a graph with a weight function. That is, it assigns an integer weight to every edge. There are multiple uses for edge weights for a graph − Network Connection Latency  Road Network Distances The Strength of a social network interaction ... Read More

Algorithms concerning graph search algorithms traverse a graph in pursuit of broad discovery or targeted search. These algorithms cut pathways across the network, but no one expects those paths to be computationally optimum. Pathfinding algorithms are assembled on graph search techniques as well as these investigate pathways amongst vertices, beginning at a specific node and going via connections till the goal is visited. What Are Graphs? Graphs are data structures that reflect "connections" among sets of components. These items are known as nodes. Edges are the connections between nodes. Shortest Path The Shortest Path algorithms locate the shortest paths or ... Read More

In this article, we'll examine a C++ procedure for ascendingly sorting an array of numerical string values. Sorting is a basic operation that entails organizing elements in a predetermined order. Because they are character-based strings that represent numbers, and these numerical strings provide a special set of challenges when it is related to sorting. The issue statement, a method and algorithm for solving it, a C++ implementation, a complexity reasoning of the provided approach, and a summary of the main points will all be covered. Problem Statement Consider a vector containing numerical strings, the aim is to arrange them in ... Read More