What is an approximation bound?
Conditions
- Used for minimization or maximization problems.
- Expresses a worst-case guarantee relative to the optimum.
Reasoning, step by step
- Define the algorithm's cost and the optimal cost .
- Establish a bound .
- For minimization, ensure .
- For maximization, ensure .
Example
The narrator introduces an approximation bound and uses the number 2 as a tangible example, stating that a 2-approximation means the algorithm's cost is never more than twice the optimal cost in the worst case.
Common misconceptions
- Thinking the bound applies only to average cases.
- Assuming the bound is a fixed number regardless of input size.
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