Contraction Algorithm

OverviewDesign and Analysis

of Algorithms I

Tim Roughgarden

Goals for These Lectures• Further practice with randomized algorithms– In a new application domain (graphs)

• Introduction to graphs and graph algorithms

Tim Roughgarden

Graphs

Tim Roughgarden

Cuts of Graphs

𝑛𝑛2

2𝑛

𝑛𝑛

Roughly how many cuts does a graph with vertices have?

Tim Roughgarden

The Minimum Cut Problem

1234

What is the number of edges crossing a minimum cut in the graph shown below?

Tim Roughgarden

A Few Applications