How do you write the approximation guarantee formally using C, C*, and rho(n)?
Conditions
- C is the algorithm-produced cost.
- C* is the true optimal cost.
- rho(n) is the approximation bound.
Reasoning, step by step
- Identify the problem type (minimization or maximization).
- Define C, C*, and rho(n).
- Apply the appropriate inequality based on the problem type.
Example
The narrator states: "For minimization problems, our cost C is always less than or equal to our bound multiplied by the optimal cost C star." and "For maximization problems, it's just flipped. Our score is at least the optimal score divided by that bound."
Common misconceptions
- Using the same inequality for both minimization and maximization.
- Forgetting that rho(n) depends on the input size n.
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