Lecture 012

Ada's Lecture

Approximation Algorithms

VERTEXT-COVER: find minimum vertex that covers all the edges (NP-complete)

Decision vs. Optimization

Decision vs. Optimization


APPROX-VERTEX-COVER: at most how many vertices used to cover all edges

TSP: traveling salesman problem

TSP Image Recovery

TSP Image Recovery

MAX-CUT: 2 coloring of vertices maximizing the number of cut edges

Minimization vs Maximization

Minimization vs Maximization

Sutner's Lecture

Minimization problem

optimal value: \text{optval}(x) = \text{min}(\text{cost}(z) | z \in \text{sol}(x))

performance ratio: \frac{\text{cost}(A(x))}{\text{optval}(x)} \geq 1

k-approximation: \text{cost}(A(x)) \leq k \times \text{optval}(x)

Lemma (P \lneq NP): let f be a polynomial time computable function. Then there is no (1 + f(x))-approximation algorithm for general TSP.

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