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Massachusetts Institute of Technology

Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall 2014)

Massachusetts Institute of Technology via MIT OpenCourseWare


Course Features
  • Video lectures
  • Captions/transcript
  • Lecture notes
  • Projects (no examples)
  • Assignments: problem sets with solutions
Educator Features
  • Instructor insights
Course Description

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P≠NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).


1. Overview.
2. 3-Partition I.
3. 3-Partition II.
4. SAT I.
5. SAT Reductions.
6. Circuit SAT.
7. Planar SAT.
8. Hamiltonicity.
9. Graph Problems.
10. Inapproximabililty Overview.
11. Inapproximability Examples.
12. Gaps and PCP.
13. W Hierarchy.
14. ETH and Planar FPT.
15. #P and ASP.
16. NP and PSPACE Video Games.
17. Nondeterministic Constraint Logic.
18. 0- and 2-Player Games.
19. Unbounded Games.
20. Undecidable and P-Complete.
21. 3SUM and APSP Hardness.
22. PPAD.
23. PPAD Reductions.

Taught by

Prof. Erik Demaine


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