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NP Complete

21 posts

P vs NP Problems

Last Updated: 23 July 2025

In the world of computers and math, there's this puzzling question: Can every problem we quickly check be solved quickly too? We have two categories: P for problems with q...read more

Complexity-analysis

P, NP, CoNP, NP hard and NP complete | Complexity Classes

Last Updated: 23 July 2025

In computer science, problems are divided into classes known as Complexity Classes. In complexity theory, a Complexity Class is a set of problems with related complexity. ...read more

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time complexity

Algorithms-NP Complete

Subset Sum is NP Complete

Last Updated: 23 July 2025

Prerequisite: NP-Completeness, Subset Sum ProblemSubset Sum Problem: Given N non-negative integers a1...aN and a target sum K, the task is to decide if there is a subset h...read more

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Analysis of Algorithms

Prove that Collinearity Problem is NP Complete

Last Updated: 09 April 2026

Problem: Prove that Collinearity Problem is NP-Complete for n Points. An instance of the collinearity problem is a set of n points ((ax, ay), (bx, by), (cx, cy), ...).Sinc...read more

Analysis of Algorithms

Proof that SAT is NP Complete

Last Updated: 23 July 2025

SAT Problem: SAT(Boolean Satisfiability Problem) is the problem of determining if there exists an interpretation that satisfies a given boolean formula. It asks whether th...read more

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Analysis of Algorithms

Double SAT is NP Complete

Last Updated: 15 July 2025

Problem Statement: Given a formula f, the problem is to determine if f has two satisfying assignments.Explanation: An instance of the problem is an input specified to the ...read more

Analysis of Algorithms

Proof that 4 SAT is NP complete

Last Updated: 15 July 2025

4-SAT Problem: 4-SAT is a generalization of 3-SAT(k-SAT is SAT where each clause has k or fewer literals).Problem Statement: Given a formula f in Conjunctive Normal Form(C...read more

Analysis of Algorithms

Subset Equality is NP Complete

Last Updated: 23 July 2025

Subset Equality Problem: Given a set S of non-negative integer values, the problem is to identify if there is a partition of the set S into two sets X and Y, such that, th...read more

Analysis of Algorithms

Optimized Longest Path is NP Complete

Last Updated: 15 July 2025

Optimized Longest Path Problem: The optimized longest path problem states that given a graph G, of a set of vertices V and edges E, the task is to prove that there is a pa...read more

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Analysis of Algorithms

Set cover is NP Complete

Last Updated: 15 July 2025

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 a collection of subsets whose union is X, with...read more

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Analysis of Algorithms

Hitting Set problem is NP Complete

Last Updated: 15 July 2025

Prerequisite: NP CompleteProblem: Given a ground set X of elements and also a grouping collection C of subsets available in X and an integer k, the task is to find the sma...read more

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Analysis of Algorithms

Set partition is NP complete

Last Updated: 15 July 2025

Set partition problem: Set partition problem partitions an array of numbers into two subsets such that the sum of each of these two subsets is the same. Let S be a set of ...read more

Analysis of Algorithms

3-coloring is NP Complete

Last Updated: 15 July 2025

Prerequisite: NP-Completeness, Graph ColoringGraph K-coloring Problem: A K-coloring problem for undirected graphs is an assignment of colors to the nodes of the graph such...read more

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Analysis of Algorithms

Proof that Subgraph Isomorphism problem is NP-Complete

Last Updated: 15 July 2025

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

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Algorithms-NP Complete

Proof that Clique Decision problem is NP-Complete

Last Updated: 15 July 2025

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

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Algorithms-NP Complete

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