Probabilistically Checkable Proofs and Inapproximability
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  General Information
  Instructor Information
  • Name: My T. Thai
  • Office: CSE 566
  • Phone: 352-392-6842
  • Email:
  • Office Hours: W 3:00pm - 4:40pm or by appointments
  Course Description
For many optimization problems of theoretical and practical interest, it is almost unfeasible to find an exact solution unless P = NP, thus requiring techniques for obtaining near-optimal solution with theoretical performance guarantee, called approximation algorithms. One of the central questions is the hardness of approximation, that is, how tightly we can approximate the solution.

Of a great triumph of theoretical computer science is the PCP Theorem discovered in the early 1990's and it became even more important in the mid-1990's when it was shown to be extremely powerful in proving the NP-hardness of approximation. Since then, several optimal or near-optimal approximation ratios of many core NP-optimization problems have been found using this connection.

This course will focus on the connection between PCPs and approximation algorithms. In particular, the course will cover many of the inapproximability results and PCPs used to prove them, including very recent results on the cutting edge of research.

  Course Objectives

I plan to cover the following:

  • Approximation Algorithms and Ratios
  • Inapproximability Proofs
  • Probabilistically Checkable Proofs (PCPs) and The PCP connection
  • Study Several Inapproximability Results, both classic and recent results
  • If time allows, the Dinur's proof of PCPs, The Unique Games Conjecture, and Expander Graphs
  • There is no formal prerequisite for this course. However, students should have a solid background in algorithms and the theory of NP-completeness. Knowing approximation algorithms is a plus.
  • Not surprisingly, no textbook is used in this course. Instead, a list of related papers will be provided along with my notes
  Grading Policies
  • Homework Assignments:
    • 2 homework assignments, each weighs 20%
    • Due at the beginning of the lecture on the due date
    • No late assignment will be accepted
  • Presentation:
    • Present one paper, either selected from the list of papers or one own interest with an approval of the instructor. The presentation must include the details helping others to understand the proofs, not simply state the theorems and results.
    • Weighs 30%
  • Final Project:
    • Weighs 30%
  • Cut-off points:
    • A >= 85%, 85% > B >= 75%, 75% > C >= 65%
  Other Policies
  • Academic Integrity Policy:
  • Collaboration:
    • You may discuss with other students on solutions of homework assignments. However, you must write up solutions on your own independently
    • Cite any sources that you use to help obtain your solutions (but do not copy the sources)
CIS 6930: PCPs and Inapproximablity