Graph Algorithms with Tree Decompositions and Treewidth

Tackling computationally difficult graph problems becomes manageable when you leverage structural properties like bounded treewidth. This written guide provides a clear foundation in tree decompositions, equipping you with the techniques needed to design efficient parameterized algorithms and dynamic programming solutions for challenging networks. You will explore fundamental graph theory concepts, analyze treewidth characteristics, and learn how to transform complex optimization challenges into tractable subproblems. What you'll learn: Understand core graph terminology, tree decomposition definitions, and treewidth principles; Apply dynamic programming across tree decompositions to compute exact solutions; Solve classic NP-hard problems including Maximum Independent Set and Graph Coloring; Formulate parameterized and approximation algorithms for challenges like Steiner Tree and Longest Path; Analyze algorithmic time complexity within modern fixed-parameter tractability frameworks. The course starts with essential definitions and foundational graph concepts before progressing through systematic, step-by-step algorithmic strategies. Designed for beginners in advanced graph algorithms and computer science enthusiasts, this course requires no prior specialized background in parameterized complexity. Start reading today to expand your graph algorithm toolkit.