Is there an algorithm to perfectly fit Bezier curves of degree at most 3 to given path?

Question

I would like to know whether there exists such an algorithm to fit Bezier curves of degree at most 3 to a given path. The path represents a set of 2D points connected to each other.(piecewise linear). The problem is to perfectly fit(going through all the points) as less Bezier curves(at most degree 3) as possible. Thanks in advance.