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It means that in the worst case, the algorithm's output cost is at most twice the true optimal cost.

Conditions: The problem is a minimization problem.; The algorithm is a 2-approximation.

It means that in the worst case, the algorithm's output cost is at most twice the true optimal cost.

Conditions: The problem is a minimization problem.; The algorithm is a 2-approximation.

For minimization problems, the guarantee is $C \leq \rho(n) \cdot C^*$. For maximization problems, it is $C \geq \frac{C^*}{\rho(n)}$.

Conditions: C is the algorithm-produced cost.; C* is the true optimal cost.; rho(n) is the approximation bound.

For minimization problems, the guarantee is $C \leq \rho(n) \cdot C^*$. For maximization problems, it is $C \geq \frac{C^*}{\rho(n)}$.

Conditions: C is the algorithm-produced cost.; C* is the true optimal cost.; rho(n) is the approximation bound.

An approximation bound is a guaranteed multiplicative limit on how much worse the algorithm's result can be than the true optimum in the worst case.

Conditions: Used for minimization or maximization problems.; Expresses a worst-case guarantee relative to the optimum.

An approximation bound is a guaranteed multiplicative limit on how much worse the algorithm's result can be than the true optimum in the worst case.

Conditions: Used for minimization or maximization problems.; Expresses a worst-case guarantee relative to the optimum.