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6.890 Algorithmic Lower Bounds

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall 2014, MIT OCW). Instructor: Professor Erik Demaine. 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). (from ocw.mit.edu)

Overview


Lecture 01 - Overview
Lecture 02 - 3-Partition I
Lecture 03 - 3-Partition II
Lecture 04 - SAT I
Lecture 05 - SAT Reductions
Lecture 06 - Circuit SAT
Lecture 07 - Planar SAT
Lecture 08 - Hamiltonicity
Lecture 09 - Graph Problems
Lecture 10 - Inapproximability Overview
Lecture 11 - Inapproximability Examples
Lecture 12 - Gaps and PCP
Lecture 13 - W Hierarchy
Lecture 14 - ETH and Planar FPT
Lecture 15 - #P and ASP
Lecture 16 - NP and PSPACE Video Games
Lecture 17 - Nondeterministic Constraint Logic
Lecture 18 - 0- and 2-Player Games
Lecture 19 - Unbounded Games
Lecture 20 - Undecidable and P-Complete
Lecture 21 - 3SUM and APSP Hardness
Lecture 22 - PPAD
Lecture 23 - PPAD Reductions

References
Algorithmic Lower Bounds: Fun with Hardness Proofs, Fall 2014
Instructor: Professor Erik Demaine. Lecture Notes. Assignments and Solutions. Projects (no examples). A class taking a practical approach to proving problems can't be solved efficiently.
6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall 2014)
Professor Erik Demaine. Lectures. Problem Sets. Project. Open Problems. Topics. Readings and Resources.