Lecture 1-2 (Basics)

• Polynomial Time
• Nondeterministic Turing Machine
• Decision Problem
  • Decidable Decision Problem
• Types of Problems:
  • Decision Problem
  • Search Problem
  • Optimisation Problem
• Complexity Class
  • $\mathrm{P}\subseteq \mathrm{NP}\subseteq \mathrm{P}-\mathrm{Space},\mathrm{NP}-\mathrm{Space}\subseteq \mathrm{EXPTIME}$
  • Memebership vs. Hardness vs. Completeness
• Big-O Notation
• Problems:
  • Independent Set Problem
    • Independent Set
  • Vertex Cover Problem
    • Vertex Cover
  • Clique Decision Problem
    • Clique
  • Dominating Set Problem
    • Dominating Set