# Tag Archives: NPHard

Problem Description: The Art Gallery Problem is formulated in geometry as the minimum number of guards that need to be placed in an n-vertex simple… Read More
Prerequisite: NP Complete Problem: Given a ground set X of elements and also a grouping collection C of subsets available in X and an integer… Read More
Problem: Given a ground Set X, an integer k, and a collection of subsets Si of X, the problem is to identify if there exists… Read More
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
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
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 graph G=(V,… Read More
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
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
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
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
Prerequisite: 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 Machine… Read More
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
Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible… Read More
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
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