6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall '14)

Prof. Erik Demaine     TAs: Sarah Eisenstat, Jayson Lynch


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[+] Inapproximability Intro. NP optimization problem, approximation, PTAS, APX, Log-APX, Poly-APX, PTAS-reduction, AP-reduction, strict-reduction, A-reduction, L-reduction, APX-hard. Max E3SAT-E5, Max 3SAT-3, independent set, vertex cover, dominating set.

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

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Handwritten notes, page 1/9[previous page][next page][PDF]

Handwritten notes, page 1/9[previous page][next page][PDF]

Slides, page 1/5[previous page][next page][PDF]

Slides, page 1/5[previous page][next page][PDF]