Computational Complexity Theory

  1. Advanced Topics
    1. Approximation Complexity
      1. Approximation Algorithms
        1. Approximation Ratios
          1. Performance Guarantees
          2. Approximation Classes
            1. Polynomial-Time Approximation Scheme PTAS
              1. Fully Polynomial-Time Approximation Scheme FPTAS
              2. Hardness of Approximation
                1. PCP Theorem
                  1. Inapproximability Results
                    1. Gap Problems
                  2. Parameterized Complexity
                    1. Fixed-Parameter Tractability
                      1. FPT Algorithms
                        1. Parameter Dependence
                        2. W-Hierarchy
                          1. W[1], W[2] Classes
                            1. Parameterized Reductions
                            2. Kernelization
                              1. Kernel Size Bounds
                                1. Lower Bounds
                              2. Fine-Grained Complexity
                                1. Conditional Lower Bounds
                                  1. Strong Exponential Time Hypothesis
                                    1. 3SUM Conjecture
                                    2. Tight Complexity Bounds
                                      1. Hardness Equivalences
                                      2. Communication Complexity
                                        1. Communication Models
                                          1. Deterministic Protocols
                                            1. Randomized Protocols
                                            2. Lower Bound Techniques
                                              1. Rank Method
                                                1. Discrepancy Method
                                                2. Applications to Other Areas
                                                3. Proof Complexity
                                                  1. Proof Systems
                                                    1. Resolution
                                                      1. Cutting Planes
                                                        1. Algebraic Proof Systems
                                                        2. Lower Bounds
                                                          1. Exponential Lower Bounds
                                                            1. Automatizability
                                                            2. Connections to Circuit Complexity

                                                          Previous

                                                          13. Quantum Complexity

                                                          Go to top

                                                          Back to Start

                                                          1. Introduction to Computational Complexity Theory