desirable scaling property

The desirable scaling property of an algorithm is that when input size $n$ doubles, the algorithm slows down by at most a constant factor $C$. An algorithm is poly-time if this property holds.

More rigorously, the property requires that there exist constants $c>0$ and $d>0$ such that, for every input size $n$, the running time of the algorithm has an upper bound of $c\cdot n^d$ primitive operations. By this definition, we can choose $C=2^d$.