Iterative Compression and Parameterized Graph Algorithms

Solving computationally hard graph problems requires specialized algorithmic strategies that go beyond brute-force search. This text-based course guides you step by step through iterative compression, one of the most powerful and elegant techniques in modern parameterized algorithm design. You will read detailed algorithmic breakdowns, understand formal correctness proofs, and learn how to reduce complex graph search spaces into manageable subproblems with guaranteed running-time bounds. What you'll learn: - Understand the core principles of parameterized complexity and fixed-parameter tractability - Master the step-by-step mechanics of iterative compression on foundational problems like Vertex Cover - Apply iterative compression to solve the Feedback Vertex Set problem in tournaments efficiently - Solve Feedback Vertex Set in general undirected graphs with concrete runtime analysis - Design compression routines using disjoint cut and separator techniques - Analyze running-time complexity bounds for exact and parameterized graph algorithms The course begins with fundamental definitions of graph terminology and parameterized complexity before moving into detailed, step-by-step algorithmic constructions and problem walkthroughs. This course is suitable for computer science students, software engineers, and algorithm enthusiasts looking to strengthen their theoretical problem-solving toolkit. Start reading today to master modern graph algorithm design techniques.