In this talk, we will address the following question: given an open knot $K$, what is minimal triple $(l, m, n) \in {\bf N}^3$ such that there exist real polynomials $f(t), g(t)$ and $h(t)$ of degree $l, m$ and $ n$ respectively and the map $t \mapsto (f(t), g(t), h(t))$ from ${\bf R}$ to ${\bf R}^3$ represents $K$? Here minimality is with respect to the usual lexicographic ordering in ${\bf N}^3$. Such a triple is known as the minimal degree sequence for $K$. We show that how to determine the minimal degree sequence for all 2-bridge knots and Torus knots. We shall try to obtain some bound for a general knot-type also.