Before revision:  We further show that we can assume all intervals of SEGMENT COVER to be of equal lengths, this proves another problem called BCU to be NP-hard in dimension 1. Moreover, we also deduce hardness of approximation for CONTIGUOUS SAT and show it cannot have a PTAS, unless P=NP .
After revision:  We further show that we can assume all intervals of SEGMENT COVER to be of equal lengths, this proves another problem called BCU to be NP-hard in dimension 1. Moreover, we also deduce hardness of approximation for these problems .