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A detailed proof showing how to reduce Vertex Cover to Set Cover, demonstrating that Set Cover is NP-complete.

A detailed proof showing how to reduce Vertex Cover to Hitting Set, demonstrating that Hitting Set is NP-complete.

A detailed proof showing how to reduce Vertex Cover to Flower-Search, proving that the Flower-Search problem is NP-complete.

A detailed proof showing how to reduce Vertex Cover to Dominating Set, demonstrating that Dominating Set is NP-complete.

A detailed proof showing how to reduce Subset Sum to Knapsack, demonstrating that Knapsack is NP-complete.

A detailed proof showing how to reduce SAT to Stingy SAT, demonstrating that Stingy SAT is NP-complete.

A detailed proof showing how to reduce SAT to Max SAT, demonstrating that Max SAT is NP-complete.

A detailed proof showing how to reduce SAT to Circuit Design, proving that the Circuit Design problem is NP-complete.

A detailed proof showing how to reduce Rudrata (s,t)-Path to White and Gold Path, proving that the White and Gold Path problem is NP-complete.

A detailed proof showing how to reduce Rudrata Path to the problem of finding a spanning tree with a specified set of leaves.

A detailed proof showing how to reduce Rudrata Path to the problem of finding a spanning tree with k or fewer leaves.

A detailed proof showing how to reduce Rudrata Path to Longest Path, demonstrating that Longest Path is NP-complete.

A detailed proof showing how to reduce Rudrata Cycle to Traveling Salesman Problem, demonstrating that TSP is NP-complete.

A detailed proof showing how to reduce Rudrata Cycle to Reliable Network, demonstrating that Reliable Network is NP-complete.

A detailed proof showing how to reduce Independent Set to Sparse Subgraph, demonstrating that Sparse Subgraph is NP-complete.

A detailed proof showing how to reduce Independent Set to the problem of finding both a clique and an independent set of given sizes.

A detailed proof showing how to reduce Clique to Subgraph Isomorphism, demonstrating that Subgraph Isomorphism is NP-complete.

A detailed proof showing how to reduce Clique to Maximum Common Subgraph, demonstrating that Maximum Common Subgraph is NP-complete.

A detailed proof showing how to reduce Clique to Kite, demonstrating that Kite is NP-complete.

A detailed proof showing how to reduce Clique to Dense Subgraph, demonstrating that Dense Subgraph is NP-complete.

A detailed proof showing how to reduce Clique to Clique-3, demonstrating that Clique-3 is NP-complete.

A detailed proof showing how to reduce 3-SAT to Exact 4-SAT, demonstrating that Exact 4-SAT is NP-complete.

Comprehensive detailed proofs showing how to reduce from Zero-One Equations to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Vertex Cover to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Traveling Salesman Problem to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Subset Sum to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from SAT to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Rudrata (s,t)-Path to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Rudrata Path to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Rudrata Cycle to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Independent Set to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Integer Linear Programming to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from Clique to prove other problems are NP-complete, with full correctness justifications.

Comprehensive detailed proofs showing how to reduce from 3-SAT to prove other problems are NP-complete, with full correctness justifications following the standard template.

Comprehensive detailed proofs showing how to reduce from 3D Matching to prove other problems are NP-complete, with full correctness justifications.

A detailed proof showing how to reduce 3-SAT to Partition, encoding variable assignments and clause satisfaction using subset sums.

A comprehensive reference guide showing how to use known NP-complete problems (SAT, 3-SAT, Clique, Independent Set, Vertex Cover, Subset Sum, Rudrata Path/Cycle, ILP, ZOE, 3D Matching, TSP) to prove new...

A comprehensive guide to proving NP-completeness through reductions, with step-by-step examples showing how to reduce from known NP-complete problems (like 3-SAT) to prove new problems are NP-complete.

A comprehensive introduction to Linear Programming covering problem formulation, geometric interpretation, standard forms, the Simplex method, interior-point methods, duality theory, and practical applications.

A comprehensive introduction to Linear Programming covering problem formulation, geometric interpretation, standard forms, the Simplex method, interior-point methods, duality theory, and practical applications.

An introduction to NP-hardness through the Zero-One Equations Problem, covering problem definition, NP-completeness proof, and connections to Integer Linear Programming and 3-SAT.

An introduction to NP-hardness through the Vertex Cover Problem, covering problem definition, NP-completeness proof, and connections to Independent Set and Clique problems.

An introduction to NP-hardness through the Traveling Salesman Problem (TSP), covering problem definition, NP-completeness proof, dynamic programming solution, approximation algorithms, and practical applications.

An introduction to NP-hardness through the Subset Sum Problem, covering problem definition, NP-completeness proof, pseudo-polynomial dynamic programming solution, and connections to Partition and Knapsack problems.

An introduction to NP-hardness through the Boolean Satisfiability Problem (SAT), covering problem definition, NP-completeness, Cook-Levin theorem, and reduction techniques.

An introduction to NP-hardness through the Rudrata Path and Rudrata (s,t)-Path problems, covering problem definitions, NP-completeness proofs, and connections to Hamiltonian Cycle.

An introduction to NP-hardness through the Rudrata Cycle Problem (also known as Hamiltonian Cycle), covering problem definition, NP-completeness proof, and connections to Rudrata Path and TSP.

An introduction to NP-hardness through Integer Linear Programming (ILP), covering problem definition, NP-completeness proof, relationship to Linear Programming, and practical solving methods.

An introduction to NP-hardness through the Independent Set Problem, covering problem definition, NP-completeness proof, and connections to Clique and Vertex Cover problems.

An introduction to NP-hardness through the Clique Problem, covering problem definition, NP-completeness proof via reduction from 3-SAT, and connections to other graph problems.

An introduction to NP-hardness through the 3D Matching Problem, covering problem definition, NP-completeness proof via reduction from 3-SAT, and connections to bipartite matching.

An introduction to Linear Programming, its polynomial-time solvability, and how it relates to reductions in complexity theory, including LP relaxations, duality, and reductions to/from LP.

An introduction to greedy algorithms, covering the greedy choice property, optimal substructure, common examples including activity selection, interval scheduling, and minimum spanning trees, and when greedy algorithms work.

An introduction to NP-hardness through Integer Linear Programming (ILP), covering problem definition, NP-completeness proof, relationship to Linear Programming, and practical solving methods.