Computational Complexity Theory

  1. Reducibility and NP-Completeness
    1. Polynomial-Time Reductions
      1. Many-One Reductions
        1. Definition and Properties
          1. Transitivity
          2. Turing Reductions
            1. Definition and Properties
            2. Reduction Construction Techniques
              1. Hardness Implications
              2. NP-Hardness
                1. Definition and Characterization
                  1. Problem Solving Implications
                    1. Hardness Preservation
                    2. NP-Completeness
                      1. Definition and Significance
                        1. Completeness Proof Structure
                          1. Membership in NP
                            1. Reduction from Known NP-Complete Problem
                            2. First NP-Complete Problem
                            3. Cook-Levin Theorem
                              1. Statement and Significance
                                1. Proof Strategy
                                  1. Tableau Construction
                                    1. Formula Encoding
                                    2. Historical Impact
                                    3. Classical NP-Complete Problems
                                      1. Satisfiability Problems
                                        1. Boolean Satisfiability
                                          1. 3-SAT
                                            1. 2-SAT Analysis
                                            2. Graph Problems
                                              1. Clique Problem
                                                1. Independent Set
                                                  1. Vertex Cover
                                                    1. Hamiltonian Path
                                                      1. Hamiltonian Cycle
                                                        1. Graph Coloring
                                                        2. Number Problems
                                                          1. Subset Sum
                                                            1. Partition Problem
                                                              1. Knapsack Problem
                                                              2. Optimization Problems
                                                                1. Traveling Salesperson Problem
                                                                  1. Bin Packing
                                                                  2. Reduction Chains
                                                                    1. Standard Reduction Sequences
                                                                      1. Gadget Construction Techniques

                                                                  Previous

                                                                  5. Time Complexity Classes

                                                                  Go to top

                                                                  Next

                                                                  7. Space Complexity Theory