How does the approximate solution compare to the optimal solution?

An approximation algorithm has a ratio bound p(n) if for any input of size n, the cost C of the approximate solution is within a factor p(n) of the cost C* of the optimal solution:

where C/C* is used for minimization problems, and C*/C for maximization problems.

Alternatively, an approximation algorithm has a relative error bound:

where (n) p(n) - 1.