Before revision:  For the BIS problem on interval graphs, we design two  \ algorithms, one parameterized by (f,k) and the other by the vertex cover number of G. Moreover, we present a 2-approximation algorithm for a slight variation of BIS on proper interval graphs .
After revision:  For the BIS problem on interval graphs, we design two  \ algorithms, one parameterized by (f,k) and the other by the vertex cover number of G. Moreover, we present a 2-approximation algorithm for a slight variation of BIS on interval graphs, we present a polynomial time approximation scheme (PTAS) and an O(n\log n) time 2-approximation algorithm .