NP-Complete Problems

Why it matters

NPC framework classifies hardness. Understanding shapes algorithm approach.

The architecture

Problem in NP.

Every NP problem reduces to it in poly time.

SAT proven first (Cook-Levin 1971).

How it works end to end

Cook 1971 + Levin 1973 independently.

Karp's 21 NP-complete problems (1972).

Standard technique: reduce known NPC to new problem.