**CS 332: Algorithms**

**Administrivia**

**Administrivia**

**Review: Tractibility**

**Review: P**

**Review: NP**

**Review: P And NP Summary**

**Review: NP-Complete Problems**

**Review: Reduction**

**An Aside: Terminology**

**NP-Hard and NP-Complete**

**Why Prove NP-Completeness?**

**Proving NP-Completeness**

**Directed Hamiltonian Cycle Þ**

Undirected Hamiltonian Cycle

**Transformation:**

Directed Þ Undirected Ham. Cycle

**Undirected Hamiltonian Cycle**

**Hamiltonian Cycle Þ TSP**

**Hamiltonian Cycle Þ TSP**

**The TSP**

**The SAT Problem**

**Conjunctive Normal Form**

**The 3-CNF Problem**

**3-CNF ® Clique**

**3-CNF ® Clique**

**3-CNF ® Clique**

**3-CNF ® Clique**

**Clique ® Vertex Cover**

**Clique ® Vertex Cover**

**Clique ® Vertex Cover**

**Clique ® Vertex Cover**

**General Comments**

**Other NP-Complete Problems**

**The End**