Typically, the integrality gap translates into the approximation ratio of an approximation algorithm. This is because an approximation algorithm relies on some rounding strategy that finds, for every relaxed solution of size formula_7, an integer solution of size at most formula_10 (where "RR" is the rounding ratio). If there is an instance with integrality gap "IG", then "every" rounding strategy will return, on that instance, a rounded solution of size at least formula_11. Therefore necessarily formula_12. The rounding ratio "RR" is only an upper bound on the approximation ratio, so in theory the actual approximation ratio may be lower than "IG", but this may be hard to prove. In practice, a large "IG" usually implies that the approximation ratio in the linear programming relaxation might be bad, and it may be better to look for other approximation schemes for that problem.