6.892 Algorithmic Lower Bounds: Fun with Hardness Proofs (Spring 2019)

This lecture begins a series on inapproximability — proving the impossibility of approximation algorithms. I'll give a brief overview of most of the typical approximation factor upper and lower bounds in the world of graph algorithms. Then we'll introduce a bunch of general concepts, including new complexity classes (NPO, PTAS, APX, Log-APX, etc.) and stronger notions of reductions that preserve approximability (PTAS-, AP-, strict-, A-, and L-reductions). Finally, we'll prove APX-hardness for a bunch of APX-complete problems:

• Max 3SAT-3
• Independent set
• Vertex cover
• Dominating set