Reductions STUDY GUIDE

Terminology and Basics

• Why reduce? To determine if we can solve problems and to determine how efficiently we can solve problems.
• What is the definition? Problem X reduces to problem Y if you can use an algorithm that solves Y to help solve X. Which means: Cost of solving X = total cost of solving Y + cost of reduction.
• What does reduction tell us?
• How to classify problems using reduction? To prove two problems have the same complexity, reduce problem X to problem Y AND reduce problem Y to problem X.

• Element distinctness reduces to sorting means that
  the cost of solving element distinctness = the cost of solving sorting + cost of reduction (checking if two adjacent elements are distinct)
• Finding the median reduces to sorting means that
  the cost of finding the median = the cost of sorting + the cost of reduction (finding the midmost element)
• What are some other examples? And what is the cost of reduction in each case?

Recommended Problems

C level

1. Textbook 6.61
2. Textbook 6.62
3. Fall 2014 Final, #12c

B level

1. Spring 2015 Final, #10a
2. Spring 2015 Final, #12a

A level

1. Spring 2015 Final, #12b
2. Fall 2014 Final, #12a
3. Fall 2014 Final, #12b