Before revision:  Our breakthrough to achieve the linear size is a new random sampling technique (for the configuration space) that employs relatively many local conflicts to prevent relatively few global conflicts. We believe this new random sampling technique has its own merit for further applications .
After revision:  Our breakthrough to achieve the linear size is a new random sampling technique for the analysis of geometric structures. Since our new technique provides a new way to develop and analyze geometric algorithms, we believe it is of independent interest .