APX-Hard Problems

Why it matters

APX classifies hardness of approximation. Understanding shapes algorithm design.

The architecture

APX: problems with constant-factor approx.

APX-hard: reduce from APX-hard problem via L-reductions.

How it works end to end

L-reduction: preserves approximation.

PCP theorem gives APX-hard base.

Cannot approximate better than constant unless P=NP.