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Proof that Independent Set in Graph theory is NP Complete

Last updated: 13 July 2022

Prerequisite: NP-Completeness, Independent set.An Independent Set S of graph G = (V, E) is a set of vertices such that no two vertices in S are adjacent to each other. It ...read more

Algorithms-NP Complete

Proof that Hamiltonian Cycle is NP-Complete

Last updated: 16 December 2022

Prerequisite: NP-Completeness, Hamiltonian cycle.Hamiltonian Cycle:A cycle in an undirected graph G=(V, E) traverses every vertex exactly once.Problem Statement: Given a g...read more

Algorithms-NP Complete

Proof that Clique Decision problem is NP-Complete

Last updated: 13 July 2022

Prerequisite: NP-CompletenessA clique is a subgraph of a graph such that all the vertices in this subgraph are connected with each other that is the subgraph is a complete...read more

Algorithms-NP Complete

Similar Topics

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470+ articles

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Proof that Subgraph Isomorphism problem is NP-Complete

Last updated: 13 June 2020

Subgraph Isomorphism Problem: We have two undirected graphs G1 and G2. The problem is to check whether G1 is isomorphic to a subgraph of G2.Graph Isomorphism: Two graphs A...read more

Algorithms-NP Complete

Proof that traveling salesman problem is NP Hard

Last updated: 04 June 2020

Pre-requisite: Travelling Salesman Problem, NP HardGiven a set of cities and the distance between each pair of cities, the travelling salesman problem finds the path betw...read more

Advanced Data Structure

Difference between NP hard and NP complete problem

Last updated: 05 January 2023

Prerequisite: NP-CompletenessNP Problem:The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in ...read more

Computer Subject

Algorithms-NP Complete

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Proof that vertex cover is NP complete

Last updated: 03 August 2018

Prerequisite - Vertex Cover Problem, NP-CompletenessProblem - Given a graph G(V, E) and a positive integer k, the problem is to find whether there is a subset V’ of vertic...read more

Theory of Computation

Algorithms-NP Complete

Engineering Mathematics

Traveling Salesman Problem (TSP) Implementation

Last updated: 31 January 2023

Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every ...read more

Shortest Superstring Problem

Last updated: 21 September 2023

Given a set of n strings arr[], find the smallest string that contains each string in the given set as substring. We may assume that no string in arr[] is substring of ano ...read more

Greedy Approximate Algorithm for Set Cover Problem

Last updated: 14 June 2023

Given a universe U of n elements, a collection of subsets of U say S = {S1, S2...,Sm} where every subset Si has an associated cost. Find a minimum cost subcollection of S ...read more

Vertex Cover Problem (Dynamic Programming Solution for Tree)

Last updated: 30 April 2023

A vertex cover of an undirected graph is a subset of its vertices such that for every edge (u, v) of the graph, either ‘u’ or ‘v’ is in vertex cover. Although the name is ...read more

Dynamic Programming

Introduction and Approximate Solution for Vertex Cover Problem

Last updated: 22 March 2023

A vertex cover of an undirected graph is a subset of its vertices such that for every edge (u, v) of the graph, either 'u' or 'v' is in the vertex cover. Although the name...read more

Approximate solution for Travelling Salesman Problem using MST

Last updated: 28 November 2022

We introduced Travelling Salesman Problem and discussed Naive and Dynamic Programming Solutions for the problem in the previous post,. Both of the solutions are infeasible...read more

Travelling Salesman Problem using Dynamic Programming

Last updated: 19 April 2023

Travelling Salesman Problem (TSP):Given a set of cities and the distance between every pair of cities, the problem is to find the shortest possible route that visits every...read more

Dynamic Programming

Introduction to NP-Complete Complexity Classes

Last updated: 05 September 2023

NP-complete problems are a subset of the larger class of NP (nondeterministic polynomial time) problems. NP problems are a class of computational problems that can be solv...read more