Course Info
Lectures
- Introduction
- NP-Optimization Problems, Approximation [V Ch1]
- Combinatorial Algorithms
- Greedy Algorithms: Vertex Cover [V Ch1]
- Layering Technique: Weighted Vertex Cover [V Ch2]
- Greedy and LP Rounding: Set Cover [V Ch2], [WS Ch1.2,1.3]
- Gap-Introducing Reductions: TSP and Metric TSP [V Ch3]
- Steiner Tree and Max Cut [V Ch3, 4]
- Parametric Pruning: k-Center [V Ch5], [WS Ch2.2]
- Polynomial-Time Approximation Schemes
- Shifted-Grid Technique: Disjoint Unit Squares [Hochbaum-Maass' paper]
- FPTAS and Strongly NP-Hardness: Knapsack [V Ch8]
- Asymptotic PTAS: Bin Packing [V Ch9]
- PTAS for Euclidean TSP [V Ch11]
- LP-Based Algorithms
- Introduction to LP and Duality [V Ch12]
- LP Rounding and Integrality Gap: Set Cover [V Ch14]
- Ellipsoid Method: Job Scheduling [WS Ch4.1-4.3]
- LP Rounding: Prize-Collecting Steiner Tree [WS Ch4.4, 5.7]
- Derandomization and Biased Flipping: MAX SAT [WS Ch5.1-5.3]
- Combined Randomization and Dual Fitting [WS Ch5.4, 5.5], V [V Ch13]
- Introduction to Primal-Dual Method: Verex Cover and Set Cover [V Ch15], [WS Ch7.1]
- Primal-Dual Method: Shortest Path and Steiner Forest [WS Ch7.3, 7.4], [V Ch22]
- Semidefinite Programming: Max Cut [WS Ch6.1, 6.2], [V Ch26]
References