# Tag Archives: NPHard

## Proof that Clique Decision problem is NP-Complete | Set 2

Prerequisite: NP-Completeness, Clique problem. A clique in a graph is a set of vertices where each vertex shares an edge with every other vertex. Thus,… Read More »

## Proof that Independent Set in Graph theory is NP Complete

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… Read More »

## Proof that Hamiltonian Cycle is NP-Complete

Prerequisite: NP-Completeness, Hamiltonian cycle. Hamiltonian Cycle: A cycle in an undirected graph G =(V, E) which traverses every vertex exactly once. Problem Statement:Given a graph… Read More »

## Proof that Clique Decision problem is NP-Complete

Prerequisite: NP-Completeness A clique is a subgraph of a graph such that all the vertices in this subgraph are connected with each other that is… Read More »

## Proof that Subgraph Isomorphism problem is NP-Complete

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.… Read More »

## Proof that Dominant Set of a Graph is NP-Complete

Pre-requisite: Dominant Set of a Graph, NP-Complete A dominating set in a graph G = (V, E) is a subset of vertices V’ following the… Read More »

## Proof that traveling salesman problem is NP Hard

Pre-requisite: Travelling Salesman Problem, NP Hard Given a set of cities and the distance between each pair of cities, the travelling salesman problem finds the… Read More »

## Difference between NP hard and NP complete problem

Prerequiste: NP-Completeness NP Problem: The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic… Read More »

## Proof that vertex cover is NP complete

Prerequisite – Vertex Cover Problem, NP-Completeness Problem – Given a graph G(V, E) and a positive integer k, the problem is to find whether there… Read More »

## Traveling Salesman Problem (TSP) Implementation

Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair of cities, the problem is to find the shortest possible route… Read More »

## Exact Cover Problem and Algorithm X | Set 2 (Implementation with DLX)

In the article Exact Cover Problem and Algorithm X | Set 1 we discussed the Exact Cover problem and Algorithm X to solve the Exact… Read More »

## Exact Cover Problem and Algorithm X | Set 1

If you have ever tried to create a program for solving Sudoku, you might have come across the Exact Cover problem. In this article, we… Read More »

## Shortest Superstring Problem

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… Read More »

## Set Cover Problem | Set 1 (Greedy Approximate Algorithm)

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… Read More »

## Vertex Cover Problem | Set 2 (Dynamic Programming Solution for Tree)

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’… Read More »