Csc5160: Combinatorial Optimization and Approximation Algorithms Topic: Graph Partitioning Problems 18.1 Graph Partitioning Problems 18.1.2 Multiway Cut

This lecture gives a general introduction of graph partitioning problems. We will begin with the definitions of some classic graph partitioning problems (e.g. multiway cut, multicut, sparsest cut), and discuss their relationships. Then we will focus on deriving two approximation algorithms. For the multiway cut problem, we will show a 2-approximation algorithm through a combinatorial argument. For the multicut problem, we will present an O(log k)-approximation algorithm using an LP-based approach, where k is the number of source-sink pairs (commodities).