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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
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