The lecture starts with an outline of the topics proposed to be covered, followed by an introduction to greedy algorithms illustrated using the set cover problem (logarithmic ratio approximation). The homework assigned was to analyze the greedy method applied to Uncapacitated Facility Location, and the Generalized Steiner Forest problems.

The lecture starts with an outline of the topics proposed to be covered, followed by an introduction to greedy algorithms illustrated using the set cover problem (logarithmic ratio approximation). The homework assigned was to analyze the greedy method applied to Uncapacitated Facility Location, and the Generalized Steiner Forest problems.

The Local Search method was illustrated using three problems: Maximum cut (2-approximation), Maximum leaf spanning trees (10-approximation) and the metric k-median problem (3-approximation).

Linear and integer programs were introduced and simple deterministic rounding was demonstrated for the vertex cover problem (2-approximation). The homework assigned was to design a deterministic rounding algorithm for the prize-collecting vertex cover problem.

Two LP-based methods were covered. Filtering the optimal LP solution was illustrated to design a constant factor approximation for the metric uncapacitated facility location problem. The primal-dual method was illustrated by designing a 2-approximation algorithm for the generalized Steiner forest problem.

Two LP-based methods were covered. Filtering the optimal LP solution was illustrated to design a constant factor approximation for the metric uncapacitated facility location problem. The primal-dual method was illustrated by designing a 2-approximation algorithm for the generalized Steiner forest problem.

LP relaxations interpreted as metrics (or distance functions in graphs) are useful in designing approximation algorithms for cut problems. This was illustrated by designing an exact algorithm for minimum s-t cut, a 2-approximation for multiway cut in graphs, a 2-approximation for the multicut problem in trees and finally a logarithmic approximation for the multicut problem in general graphs.