Prove Dense Subgraph is NP-Complete by Generalisation

Satadru Jati
Updated on 09-Oct-2023 12:32:56

433 Views

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

Prove Clique and Independent Set Problem is NP-Complete

Satadru Jati
Updated on 09-Oct-2023 12:31:10

1K+ Views

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

Prove that Sparse Graph is NP-Complete

Satadru Jati
Updated on 09-Oct-2023 12:26:00

409 Views

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

Minimize Colors to Paint Graph Such That No Path Has Same Color

Satadru Jati
Updated on 09-Oct-2023 12:24:08

290 Views

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

Monotonic Shortest Path from Source to Destination in Directed Weighted Graph

Satadru Jati
Updated on 09-Oct-2023 12:21:33

680 Views

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

Find Remaining Vertices in Graph After Marking Shortest Path for Neighbours

Satadru Jati
Updated on 09-Oct-2023 12:14:53

166 Views

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

Linear Filtering Without Using imfilter Function in MATLAB

Manish Kumar Saini
Updated on 09-Oct-2023 11:15:19

407 Views

In MATLAB, "linear filtering" is a technique used to apply a linear filter to a digital image. The fundamental principle behind the working of linear filtering is convolution. This article is meant for explaining the concept of linear filtering and how to perform linear filtering without using the "imfilter" function in MATLAB. What is Linear Filtering? In digital image processing, the process of applying a linear filter (also called convolution kernel) to a digital image is called linear filtering. The working of linear filtering is based on the concept of convolution. In the process of linear filtering, a convolution ... Read More

Reverse a String in MATLAB

Manish Kumar Saini
Updated on 09-Oct-2023 11:14:27

435 Views

MATLAB provides various built-in functions to reverse a string of text. In this tutorial, I am going to explain all the commonly used methods to reverse a string in MATLAB. Reverse a String Using "reverse" Function in MATLAB There is a built-in function "reverse" in MATLAB that we can use to reverse a string. Syntax reversed_string = reverse(string); The steps involved in reversing a string using the "reverse" function are given below − Step (1) − Create a string of text. Step (2) − Call the "reverse" function to reverse the string. Step (3) − Display the ... Read More

Reverse a Number in MATLAB

Manish Kumar Saini
Updated on 09-Oct-2023 11:11:42

835 Views

In MATLAB, there are various methods and functions for reversing a given number. In this tutorial, I will explain all these methods one-by-one with the help of examples. Reverse a Number Using "fliplr" Function in MATLAB The "fliplr" is a built-in function in MATLAB that we can use to reverse a given number. Syntax reversed_num = fliplr(number); Here, the "number" must be a string. Here are the steps involved in reversing a given number using the "fliplr" function in MATLAB. Step (1) − Input the number. Step (2) − Convert the input number to a string. For ... Read More

Remove Spaces in a String in MATLAB

Manish Kumar Saini
Updated on 09-Oct-2023 11:09:54

657 Views

MATLAB provides various methods and functions to remove spaces in a string. In this tutorial, we will cover the commonly used methods for removing extra spaces in a string. So, let’s start. Remove White Space in a String Using "isspace" Function In MATLAB, the "isspace" function is a built-in function that is used to determine and remove the ASCII white space present in a string. Syntax string_without_space = isspace('input_string'); Example Let us take an example in MATLAB programming to use this function to remove white spaces in a string. % MATLAB code to remove white space from ... Read More

Advertisements