Here’s a list of 100 chapter titles for Approximation Algorithms tailored for competitive programming, progressing from beginner to advanced levels:
- Introduction to Approximation Algorithms: Concepts and Motivation
- Basics of Optimization Problems: P vs. NP
- Approximation Ratios: Definitions and Examples
- Greedy Algorithms: Basics and Examples
- Greedy Algorithms for Set Cover
- Greedy Algorithms for Knapsack Problems
- Greedy Algorithms for Scheduling Problems
- Greedy Algorithms for Graph Coloring
- Greedy Algorithms for Minimum Spanning Trees
- Greedy Algorithms for Shortest Path Problems
- Greedy Algorithms for Maximum Cut Problems
- Greedy Algorithms for Vertex Cover
- Greedy Algorithms for Traveling Salesman Problem (TSP)
- Greedy Algorithms for Bin Packing
- Greedy Algorithms for Job Scheduling
- Greedy Algorithms for Facility Location
- Greedy Algorithms for Load Balancing
- Greedy Algorithms for Network Design
- Greedy Algorithms for Clustering
- Greedy Algorithms for Submodular Maximization
- LP Relaxation: Basics and Examples
- LP Relaxation for Set Cover
- LP Relaxation for Vertex Cover
- LP Relaxation for Knapsack Problems
- LP Relaxation for Scheduling Problems
- LP Relaxation for Graph Coloring
- LP Relaxation for Minimum Spanning Trees
- LP Relaxation for Shortest Path Problems
- LP Relaxation for Maximum Cut Problems
- LP Relaxation for Traveling Salesman Problem (TSP)
- LP Relaxation for Bin Packing
- LP Relaxation for Job Scheduling
- LP Relaxation for Facility Location
- LP Relaxation for Load Balancing
- LP Relaxation for Network Design
- LP Relaxation for Clustering
- LP Relaxation for Submodular Maximization
- Randomized Rounding: Basics and Examples
- Randomized Rounding for Set Cover
- Randomized Rounding for Vertex Cover
- Randomized Rounding for Knapsack Problems
- Randomized Rounding for Scheduling Problems
- Randomized Rounding for Graph Coloring
- Randomized Rounding for Minimum Spanning Trees
- Randomized Rounding for Shortest Path Problems
- Randomized Rounding for Maximum Cut Problems
- Randomized Rounding for Traveling Salesman Problem (TSP)
- Randomized Rounding for Bin Packing
- Randomized Rounding for Job Scheduling
- Randomized Rounding for Facility Location
- Primal-Dual Methods: Basics and Examples
- Primal-Dual Methods for Set Cover
- Primal-Dual Methods for Vertex Cover
- Primal-Dual Methods for Knapsack Problems
- Primal-Dual Methods for Scheduling Problems
- Primal-Dual Methods for Graph Coloring
- Primal-Dual Methods for Minimum Spanning Trees
- Primal-Dual Methods for Shortest Path Problems
- Primal-Dual Methods for Maximum Cut Problems
- Primal-Dual Methods for Traveling Salesman Problem (TSP)
- Primal-Dual Methods for Bin Packing
- Primal-Dual Methods for Job Scheduling
- Primal-Dual Methods for Facility Location
- Primal-Dual Methods for Load Balancing
- Primal-Dual Methods for Network Design
- Primal-Dual Methods for Clustering
- Primal-Dual Methods for Submodular Maximization
- Semidefinite Programming (SDP): Basics and Examples
- SDP for Maximum Cut Problems
- SDP for Graph Coloring
- SDP for Traveling Salesman Problem (TSP)
- SDP for Clustering
- SDP for Submodular Maximization
- SDP for Facility Location
- SDP for Load Balancing
- SDP for Network Design
- SDP for Scheduling Problems
- SDP for Knapsack Problems
- SDP for Vertex Cover
- SDP for Set Cover
- SDP for Minimum Spanning Trees
- SDP for Shortest Path Problems
- SDP for Bin Packing
- SDP for Job Scheduling
- SDP for Submodular Maximization
- SDP for Clustering
- SDP for Facility Location
- SDP for Load Balancing
- SDP for Network Design
- SDP for Scheduling Problems
- SDP for Knapsack Problems
- SDP for Vertex Cover
- SDP for Set Cover
- SDP for Minimum Spanning Trees
- SDP for Shortest Path Problems
- SDP for Bin Packing
- SDP for Job Scheduling
- SDP for Submodular Maximization
- SDP for Clustering
- SDP for Facility Location
This progression covers foundational concepts, intermediate techniques, and advanced topics, ensuring a comprehensive understanding of approximation algorithms in competitive programming.