Strongly-polynomial time

In computer science, a polynomial-time algorithm is - generally speaking - an algorithm whose running time is upper-bounded by some polynomial function of the input size. The definition naturally depends on the computational model, which determines how the running time is measured, and how the input size is measured. Two prominent computational models are the Turing-machine model and the arithmetic model. A strongly-polynomial time algorithm is polynomial in both models, whereas a weakly-polynomial time algorithm is polynomial only in the Turing machine model.

The difference between strongly- and weakly-polynomial time is when the inputs to the algorithms consist of integer or rational numbers. It is particularly common in optimization.